Integrate Numerically using Simpsons Rule

AIM: Write a Python program to integrate numerically using Simpsons rule.

Source Code:

# Simpson's 1/3 Rule

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

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

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

Output:

Enter lower limit of integration: 1
Enter upper limit of integration: 8
Enter number of sub intervals: 6
Integration result by Simpson's 1/3 method is: 0.667126