/*----------------------------------------------------------------*/
/*  Program chapter4_8        					  */
/* 							          */
/*  This program estimates the area under a given curve using     */
/*  trapezoids with equal bases.				  */

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

int main(void)
{
   /*  Declare variables and function prototypes.  */
   int num_trapezoids;
   double a, b, area;
   double integrate(double a, double b, int n);

  /*  Get input from user.  */
   printf("Enter the interval enpoints, a and b\n");
   scanf("%lf %lf", &a, &b);
   printf("Enter the number of trapezoids\n");
   scanf("%d", &num_trapezoids);

   /*  Estimate area under the curve of 4e^-x  */
   area = integrate(a, b, num_trapezoids);

   /*  Print result.  */
   printf("Using %d trapezoids, the estimated area is %f\n",
		num_trapezoids, area);

   return 0;
}

double integrate(double a, double b, int n)
{
	double sum = 0, x, base, area;
	double f(double x);
	int k;

	base = (b-a)/n;
	for(k=2; k<=n; k++)
	{
		x = a + base*(k-1);
		sum = sum + f(x);
	}
	area = 0.5*base*(f(a) + 2*sum + f(b));
	return area;
}
double f(double x)
{
	return(4*exp(-x));
}