c program to implement numerical integration using simpson 3/8 rule

 code:

#include <stdio.h>

#include <math.h>

double f(double x) {

  return exp(x);

}

double simpson38(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 % 3 == 0) {

      sum += 2 * f(a + i * h);

    } else {

      sum += 3 * f(a + i * h);

    }

  }

  return (3 * h / 8) * sum;

}

int main() {

  double a = 0;

  double b = 1;

  int n = 10;

  double integral = simpson38(a, b, n);

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

  return 0;

}

output :

The integral of exp(x) from 0 to 1 is 1.718282