TheAlgorithms-C/numerical_methods/simpsons_1-3rd_rule.c

#include <stdio.h>
#include <math.h>

float f(float x)
{
	return 1.0 + x * x * x; //This is the expresion of the function to integrate?
}

int main()
{
	int i, n;
	float a, b, h, x, s2, s3, sum, integral;

	printf("enter the lower limit of the integration:");
	scanf("%f", &a);
	printf("enter the upper limit of the integration:");
	scanf("%f", &b);
	printf("enter the number of intervals:");
	scanf("%d", &n);

	h = (b - a) / n;
	sum = f(a) + f(b);
	s2 = s3 = 0.0;

	for (i = 1; i < n; i += 3)
	{
		x = a + i * h;
		s3 = s3 + f(x) + f(x + h);
	}

	for (i = 3; i < n; i += 3)
	{
		x = a + i * h;
		s2 = s2 + f(x);
	}

	integral = (h / 3.0) * (sum + 2 * s2 + 4 * s3);
	printf("\nValue of the integral = %9.4f\n", integral);

	return 0;
}