/*-----------------------------------------------------------------------------*/
/*  Program chapter5_9                                                         */
/*                                                                             */
/*  This program estimates the area under a given curve                        */
/*  using trapezoids with equal bases.                                         */

#include <iostream>
#include <cmath>
using namespace std;

//  Function prototypes.  
double integrate(double a, double b, int n);
double f(double x);

int main()
{
   //  Declare objects
   int num_trapezoids;
   double a, b, area;

   //  Get input from user.  
   cout << "Enter the interval endpoints, a and b\n";
   cin >> a >> b;
   cout << "Enter the number of trapezoids\n";
   cin >> num_trapezoids;
   //  Estimate area under the curve of 4e^-x  
   area = integrate(a, b, num_trapezoids);

   //  Print result.
   cout << "Using " << num_trapezoids << " trapezoids, the estimated area is "
        << area << endl;

   return 0;
}
/*-----------------------------------------------------------------------------*/

/*-----------------------------------------------------------------------------*/
double integrate(double a, double b, int n)
{
   //  Declare objects.
        double sum = 0, x, base, area;

        base = (b-a)/n;
        for(int 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));
}
/*-----------------------------------------------------------------------------*/