# C++ program to implement Simpson’s 3/8 rule

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In this tutorial, we will be discussing a program to implement SImpson’s ⅜ rule.

Simpson’s ⅜ rule is used for doing numerical integrations. The most common use case of this method is in performing numerical approximations of definite integrals.

In this, the parabolas on the graph are used for performing the approximations.

## Example

#include<iostream>
using namespace std;
//function that is to be integrated
float func_inte( float x){
return (1 / ( 1 + x * x ));
}
//calculating the approximations
float func_calculate(float lower_limit, float upper_limit, int
interval_limit ){
float value;
float interval_size = (upper_limit - lower_limit) / interval_limit;
float sum = func_inte(lower_limit) + func_inte(upper_limit);
for (int i = 1 ; i < interval_limit ; i++) {
if (i % 3 == 0)
sum = sum + 2 * func_inte(lower_limit + i * interval_size);
else
sum = sum + 3 * func_inte(lower_limit + i * interval_size);
}
return ( 3 * interval_size / 8 ) * sum ;
}
int main(){
int interval_limit = 8;
float lower_limit = 1;
float upper_limit = 8;
float integral_res = func_calculate(lower_limit,
upper_limit, interval_limit);
cout << integral_res << endl;
return 0;
}

## Output

0.663129