// Approximating the area under several functions using the Trapezoidal Rule.
// Version 5:  An area function has numeric and functional parameters.

#include <iostream.h>
#include <math.h>

double circle(double x);
/* function for a circle of radius 2, centered at the origin */

double parabola(double x);
/* function for the standard parabola y = x^2 */

double area(double a, double b, int n, double f (double));
/* Approximation of area under f(x) on [a, b] using the Trapezoidal Rule */

int main (void)
{  int number;
   cout << "Program approximates the area under several functions using the "
        << "Trapezoidal Rule." << endl;
   cout << "Enter number of subintervals to be used: ";
   cin  >> number;

   cout << endl;
   cout << "Approximation of 1/4 area of circle of radius 2 is "
        << area (0.0, 2.0, number, circle) << endl << endl;
   cout << "Approximation of area under y = x^2 between 1 and 3 is "
        << area (1.0, 3.0, number, parabola) << endl << endl;
   return 0;
}

double circle(double x) 
/* function for a circle of radius 2, centered at the origin */
{  return (sqrt(4.0 - x*x));
}
 
double parabola(double x)
/* function for the standard parabola y = x^2 */
{ return x*x;
}

double area (double a, double b, int n, double f (double))
/* Finding area via the Trapezoidal Rule */
{  double width = (b - a) / n; 
   double sum = (f(a) + f(b)) / 2.0;   /* first and last terms in sum */
   double xvalue;

   for (xvalue = a + width; xvalue < b; xvalue += width)
      sum += f(xvalue);
   return (sum * width);
}