Hướng dẫn how do you write simpsons rule in python? - làm thế nào để bạn viết quy tắc simpsons trong python?

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

6

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

2

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

87

PHPSimpson 1/3 method is defined using python function definition

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Evaluate logx dx within limit 4 to 5.2. First we will divide interval into six equal parts as number of interval should be even. x : 4 4.2 4.4 4.6 4.8 5.0 5.2 logx : 1.38 1.43 1.48 1.52 1.56 1.60 1.64 Now we can calculate approximate value of integral using above formula: = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 1.60 ) +2 *(1.48 + 1.56)] = 1.84 Hence the approximation of above integral is 1.827 using Simpson's 1/3 rule. 96 d=None while(True): print("Enter your own data or enter the word "test" for ready data.\n") x=input ('Enter the beginning of the interval (a): ') if x == 'test': x=0 h=4 #krok (Δx) b=12 #granica np. 0>12 #w=(20*x)-(x**2) lub (1+x**3)**(1/2) break h=input ('Enter the size of the integration step (h): ') if h == 'test': x=0 h=4 b=12 break b=input ('Enter the end of the range (b): ') if b == 'test': x=0 h=4 b=12 break d=input ('Give the function pattern: ') if d == 'test': x=0 h=4 b=12 break elif d != -9999.9: break x=float(x) h=float(h) b=float(b) a=float(x) if d == None or d == 'test': def fun(x): return 100-(x**2)/2 #(20*x)-(x**2) else: def fun(x): w = eval(d) return w h=h/2 l=0 #just numeration print('n=',(b-x)/(h*2)) n=int((b-a)/h+1) y = [] #tablica/lista wszystkich y / list of all "y" yf = [] for i in range(n): f=fun(x) print('y%s' %(l),'=',f) y.append(f) l+=1 x+=h print(y,'\n') n1=int(((b-a)/h)/2) l=1 for i in range(n1): nf=(h/3*(y[+0]+4*y[+1]+y[+2])) y=y[2:] print('Całka dla kroku/Integral for a step',l,'=',nf) yf.append(nf) l+=1 print('\nWynik całki/Result of the integral =', sum(yf) ) 7Evaluate logx dx within limit 4 to 5.2. First we will divide interval into six equal parts as number of interval should be even. x : 4 4.2 4.4 4.6 4.8 5.0 5.2 logx : 1.38 1.43 1.48 1.52 1.56 1.60 1.64 Now we can calculate approximate value of integral using above formula: = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 1.60 ) +2 *(1.48 + 1.56)] = 1.84 Hence the approximation of above integral is 1.827 using Simpson's 1/3 rule. 98d=None while(True): print("Enter your own data or enter the word "test" for ready data.\n") x=input ('Enter the beginning of the interval (a): ') if x == 'test': x=0 h=4 #krok (Δx) b=12 #granica np. 0>12 #w=(20*x)-(x**2) lub (1+x**3)**(1/2) break h=input ('Enter the size of the integration step (h): ') if h == 'test': x=0 h=4 b=12 break b=input ('Enter the end of the range (b): ') if b == 'test': x=0 h=4 b=12 break d=input ('Give the function pattern: ') if d == 'test': x=0 h=4 b=12 break elif d != -9999.9: break x=float(x) h=float(h) b=float(b) a=float(x) if d == None or d == 'test': def fun(x): return 100-(x**2)/2 #(20*x)-(x**2) else: def fun(x): w = eval(d) return w h=h/2 l=0 #just numeration print('n=',(b-x)/(h*2)) n=int((b-a)/h+1) y = [] #tablica/lista wszystkich y / list of all "y" yf = [] for i in range(n): f=fun(x) print('y%s' %(l),'=',f) y.append(f) l+=1 x+=h print(y,'\n') n1=int(((b-a)/h)/2) l=1 for i in range(n1): nf=(h/3*(y[+0]+4*y[+1]+y[+2])) y=y[2:] print('Całka dla kroku/Integral for a step',l,'=',nf) yf.append(nf) l+=1 print('\nWynik całki/Result of the integral =', sum(yf) ) 90

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule # Define function to integrate def f(x): return 1/(1 + x**2) # Implementing Simpson's 1/3 def simpson13(x0,xn,n): # calculating step size h = (xn - x0) / n # Finding sum integration = f(x0) + f(xn) for i in range(1,n): k = x0 + i*h if i%2 == 0: integration = integration + 2 * f(k) else: integration = integration + 4 * f(k) # Finding final integration value integration = integration * h/3 return integration # Input section lower_limit = float(input("Enter lower limit of integration: ")) upper_limit = float(input("Enter upper limit of integration: ")) sub_interval = int(input("Enter number of sub intervals: ")) # Call trapezoidal() method and get result result = simpson13(lower_limit, upper_limit, sub_interval) print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) ) 1 # Simpson's 1/3 Rule # Define function to integrate def f(x): return 1/(1 + x**2) # Implementing Simpson's 1/3 def simpson13(x0,xn,n): # calculating step size h = (xn - x0) / n # Finding sum integration = f(x0) + f(xn) for i in range(1,n): k = x0 + i*h if i%2 == 0: integration = integration + 2 * f(k) else: integration = integration + 4 * f(k) # Finding final integration value integration = integration * h/3 return integration # Input section lower_limit = float(input("Enter lower limit of integration: ")) upper_limit = float(input("Enter upper limit of integration: ")) sub_interval = int(input("Enter number of sub intervals: ")) # Call trapezoidal() method and get result result = simpson13(lower_limit, upper_limit, sub_interval) print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) ) 2 1.82784703Evaluate logx dx within limit 4 to 5.2. First we will divide interval into six equal parts as number of interval should be even. x : 4 4.2 4.4 4.6 4.8 5.0 5.2 logx : 1.38 1.43 1.48 1.52 1.56 1.60 1.64 Now we can calculate approximate value of integral using above formula: = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 1.60 ) +2 *(1.48 + 1.56)] = 1.84 Hence the approximation of above integral is 1.827 using Simpson's 1/3 rule. 98 # Simpson's 1/3 Rule # Define function to integrate def f(x): return 1/(1 + x**2) # Implementing Simpson's 1/3 def simpson13(x0,xn,n): # calculating step size h = (xn - x0) / n # Finding sum integration = f(x0) + f(xn) for i in range(1,n): k = x0 + i*h if i%2 == 0: integration = integration + 2 * f(k) else: integration = integration + 4 * f(k) # Finding final integration value integration = integration * h/3 return integration # Input section lower_limit = float(input("Enter lower limit of integration: ")) upper_limit = float(input("Enter upper limit of integration: ")) sub_interval = int(input("Enter number of sub intervals: ")) # Call trapezoidal() method and get result result = simpson13(lower_limit, upper_limit, sub_interval) print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) ) 06

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

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Bàn luận 

Trong phân tích số, quy tắc Simpson 1/3 là một phương pháp xấp xỉ bằng số của các tích phân xác định. Cụ thể, đó là xấp xỉ sau: & nbsp;
the area into n equal segments of width Δx. 
Simpson’s rule can be derived by approximating the integrand f (x) (in blue) 
by the quadratic interpolant P(x) (in red). 
 

& nbsp; & nbsp;
1.Select a value for n, which is the number of parts the interval is divided into. 
2.Calculate the width, h = (b-a)/n 
3.Calculate the values of x0 to xn as x0 = a, x1 = x0 + h, …..xn-1 = xn-2 + h, xn = b. 
Consider y = f(x). Now find the values of y(y0 to yn) for the corresponding x(x0 to xn) values. 
4.Substitute all the above found values in the Simpson’s Rule Formula to calculate the integral value.
Approximate value of the integral can be given by Simpson’s Rule: 

Bàn luận 

Trong phân tích số, quy tắc Simpson 1/3 là một phương pháp xấp xỉ bằng số của các tích phân xác định. Cụ thể, đó là xấp xỉ sau: & nbsp; In this rule, n must be EVEN.
Application : 
It is used when it is very difficult to solve the given integral mathematically. 
This rule gives approximation easily without actually knowing the integration rules.
Example : 
 

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

C++

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

& nbsp; & nbsp;

Trong quy tắc 1/3 của Simpson, chúng tôi sử dụng parabolas để xấp xỉ từng phần của đường cong. & nbsp; bởi nội suy bậc hai p (x) (màu đỏ). & nbsp; & nbsp;

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Để tích hợp bất kỳ hàm f (x) nào trong khoảng (a, b), hãy làm theo các bước được đưa ra dưới đây: 1. Chọn một giá trị cho n, đó là số phần mà khoảng thời gian được chia thành. & Nbsp; 2.Calculation Chiều rộng, h = (b-a) /n 3 Hãy xem xét y = f (x). Bây giờ tìm các giá trị của y (y0 đến yn) cho các giá trị x (x0 đến xn) tương ứng. được đưa ra bởi quy tắc của Simpson: & nbsp;

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Lưu ý: Trong quy tắc này, n phải chẵn. Ứng dụng: & nbsp; nó được sử dụng khi rất khó để giải quyết tính tích phân đã cho.

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

lower_limit3lower_limit4

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

lower_limit3upper_limit0

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

lower_limit3upper_limit4

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

1.827847

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Enter lower limit of integration: 0 Enter upper limit of integration: 1 Enter number of sub intervals: 6 Integration result by Simpson's 1/3 method is: 0.785398 2 sub_interval4

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

Các

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

lower_limit3

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

lower_limit3

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

lower_limit3lower_limit1

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

lower_limit3lower_limit6 lower_limit1

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

lower_limit3lower_limit6

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Python3

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

lower_limit3

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

lower_limit3

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

lower_limit3

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

C#

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

lower_limit3

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

lower_limit3

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

Enter lower limit of integration: 0
Enter upper limit of integration: 1
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.785398

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

lower_limit3lower_limit6

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2. First we will divide interval into six equal parts as number of interval should be even. x : 4 4.2 4.4 4.6 4.8 5.0 5.2 logx : 1.38 1.43 1.48 1.52 1.56 1.60 1.64 Now we can calculate approximate value of integral using above formula: = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 1.60 ) +2 *(1.48 + 1.56)] = 1.84 Hence the approximation of above integral is 1.827 using Simpson's 1/3 rule. 6Enter lower limit of integration: 0 Enter upper limit of integration: 1 Enter number of sub intervals: 6 Integration result by Simpson's 1/3 method is: 0.785398 2 # Simpson's 1/3 Rule # Define function to integrate def f(x): return 1/(1 + x**2) # Implementing Simpson's 1/3 def simpson13(x0,xn,n): # calculating step size h = (xn - x0) / n # Finding sum integration = f(x0) + f(xn) for i in range(1,n): k = x0 + i*h if i%2 == 0: integration = integration + 2 * f(k) else: integration = integration + 4 * f(k) # Finding final integration value integration = integration * h/3 return integration # Input section lower_limit = float(input("Enter lower limit of integration: ")) upper_limit = float(input("Enter upper limit of integration: ")) sub_interval = int(input("Enter number of sub intervals: ")) # Call trapezoidal() method and get result result = simpson13(lower_limit, upper_limit, sub_interval) print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) ) 33 # Simpson's 1/3 Rule # Define function to integrate def f(x): return 1/(1 + x**2) # Implementing Simpson's 1/3 def simpson13(x0,xn,n): # calculating step size h = (xn - x0) / n # Finding sum integration = f(x0) + f(xn) for i in range(1,n): k = x0 + i*h if i%2 == 0: integration = integration + 2 * f(k) else: integration = integration + 4 * f(k) # Finding final integration value integration = integration * h/3 return integration # Input section lower_limit = float(input("Enter lower limit of integration: ")) upper_limit = float(input("Enter upper limit of integration: ")) sub_interval = int(input("Enter number of sub intervals: ")) # Call trapezoidal() method and get result result = simpson13(lower_limit, upper_limit, sub_interval) print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) ) 34d=None while(True): print("Enter your own data or enter the word "test" for ready data.\n") x=input ('Enter the beginning of the interval (a): ') if x == 'test': x=0 h=4 #krok (Δx) b=12 #granica np. 0>12 #w=(20*x)-(x**2) lub (1+x**3)**(1/2) break h=input ('Enter the size of the integration step (h): ') if h == 'test': x=0 h=4 b=12 break b=input ('Enter the end of the range (b): ') if b == 'test': x=0 h=4 b=12 break d=input ('Give the function pattern: ') if d == 'test': x=0 h=4 b=12 break elif d != -9999.9: break x=float(x) h=float(h) b=float(b) a=float(x) if d == None or d == 'test': def fun(x): return 100-(x**2)/2 #(20*x)-(x**2) else: def fun(x): w = eval(d) return w h=h/2 l=0 #just numeration print('n=',(b-x)/(h*2)) n=int((b-a)/h+1) y = [] #tablica/lista wszystkich y / list of all "y" yf = [] for i in range(n): f=fun(x) print('y%s' %(l),'=',f) y.append(f) l+=1 x+=h print(y,'\n') n1=int(((b-a)/h)/2) l=1 for i in range(n1): nf=(h/3*(y[+0]+4*y[+1]+y[+2])) y=y[2:] print('Całka dla kroku/Integral for a step',l,'=',nf) yf.append(nf) l+=1 print('\nWynik całki/Result of the integral =', sum(yf) ) 68

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Các

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

1.827847

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

1.827847

1.827847

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

1.827847

1.827847

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

1.827847

1.827847

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

1.827847

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

1.827847

lower_limit3

1.827847

1.827847

1.827847

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

1.827847

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

1.827847

1.827847

lower_limit3

1.827847

1.827847

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

1.827847

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

lower_limit3

1.827847

1.827847

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

1.827847

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

1.827847

1.827847

1.827847

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

1.827847

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

1.827847

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

1.827847

1.827847

1.827847

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

lower_limit46

JavaScript

lower_limit47

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

lower_limit3

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

lower_limit3

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

lower_limit3lower_limit1 lower_limit2

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

lower_limit3lower_limit6 lower_limit1 lower_limit8

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

lower_limit3lower_limit6

d=None
while(True):
    print("Enter your own data or enter the word "test" for ready data.\n")
    x=input ('Enter the beginning of the interval (a): ') 
    if x == 'test':
        x=0
        h=4  #krok (Δx)
        b=12 #granica np. 0>12  
        #w=(20*x)-(x**2)  lub   (1+x**3)**(1/2)
        break
    h=input ('Enter the size of the integration step (h): ')
    if h == 'test':
        x=0
        h=4 
        b=12 
        break
    b=input ('Enter the end of the range (b): ')
    if b == 'test':
        x=0
        h=4  
        b=12 
        break 
    d=input ('Give the function pattern: ')
    if d == 'test':
        x=0
        h=4  
        b=12
        break
    elif d != -9999.9:
        break

x=float(x)
h=float(h)
b=float(b)
a=float(x)

if d == None or d == 'test':
    def fun(x): 
        return 100-(x**2)/2 #(20*x)-(x**2)
else:
    def fun(x): 
        w = eval(d)
        return  w
h=h/2
l=0  #just numeration
print('n=',(b-x)/(h*2))
n=int((b-a)/h+1)
y = []   #tablica/lista wszystkich y / list of all "y"
yf = []
for i in range(n):
    f=fun(x)
    print('y%s' %(l),'=',f)
    y.append(f)
    l+=1
    x+=h
print(y,'\n')
n1=int(((b-a)/h)/2)  
l=1
for i in range(n1):
    nf=(h/3*(y[+0]+4*y[+1]+y[+2]))
    y=y[2:]
    print('Całka dla kroku/Integral for a step',l,'=',nf)
    yf.append(nf)
    l+=1
print('\nWynik całki/Result of the integral =', sum(yf) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

Evaluate logx dx within limit 4 to 5.2.

First we will divide interval into six equal 
parts as number of interval should be even.

x    :  4     4.2   4.4   4.6   4.8  5.0  5.2
logx :  1.38  1.43  1.48  1.52  1.56 1.60 1.64

Now we can calculate approximate value of integral
using above formula:
     = h/3[( 1.38 + 1.64) + 4 * (1.43 + 1.52 + 
                      1.60 ) +2 *(1.48 + 1.56)]
     = 1.84
Hence the approximation of above integral is 
1.827 using Simpson's 1/3 rule.  
          

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

# Simpson's 1/3 Rule

# Define function to integrate
def f(x):
    return 1/(1 + x**2)

# Implementing Simpson's 1/3 
def simpson13(x0,xn,n):
    # calculating step size
    h = (xn - x0) / n
    
    # Finding sum 
    integration = f(x0) + f(xn)
    
    for i in range(1,n):
        k = x0 + i*h
        
        if i%2 == 0:
            integration = integration + 2 * f(k)
        else:
            integration = integration + 4 * f(k)
    
    # Finding final integration value
    integration = integration * h/3
    
    return integration
    
# Input section
lower_limit = float(input("Enter lower limit of integration: "))
upper_limit = float(input("Enter upper limit of integration: "))
sub_interval = int(input("Enter number of sub intervals: "))

# Call trapezoidal() method and get result
result = simpson13(lower_limit, upper_limit, sub_interval)
print("Integration result by Simpson's 1/3 method is: %0.6f" % (result) )

upper_limit17

Output:  
 

1.827847