# Simpson's 1/3 Method Python Program

#### This program implements Simpson's 1/3 Rule to find approximated value of numerical integration in python programming language.

In this python program, `lower_limit` and `upper_limit` are lower and upper limit of integration, `sub_interval` is number of sub interval used while finding sum and function `f(x)` to be integrated by Simpson 1/3 method is defined using python function definition `def f(x):`.

## Python Source Code: 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) )
``````

## Output

```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
```