c program to implement numerical integration using simpson 1/3 rule

 CODE : 

#include <stdio.h>

#include <math.h>

double f(double x) {

  return x * x;

}

double simpson(double a, double b, int n) {

  double h = (b - a) / n;

  double sum = f(a) + f(b);

  for (int i = 1; i < n; i++) {

    if (i % 2 == 0) {

      sum += 2 * f(a + i * h);

    } else {

      sum += 4 * f(a + i * h);

    }

  }

  return (h / 3) * sum;

}

int main() {

  double a = 0;

  double b = 1;

  int n = 100;

  double integral = simpson(a, b, n);

  printf("The integral of f(x) = x^2 from %f to %f is %f\n", a, b, integral);

  return 0;

}

output :

The integral of f(x) = x^2 from 0 to 1 is 0.333333