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

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

const int n = 50;          /* number of subintervals to be used */

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

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

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

/* main: runs trapezoid approximation for circle and parabola
 * 
 * Preconditions: 
 *  f(x) is defined
 *  area is defined
 *
 * Postconditions: 
 *  Prints the area to terminal
 *  returns 0
 */
int main (void)
{  int number;
   printf ("Program approximates the area under a function using the ");
   printf ("Trapezoidal Rule, based on %d intervals.\n", n);

   printf ("\n");;
   printf ("Approximation of 1/4 area of circle of radius 2 is %7.5f .\n\n",
                    area (0.0, 2.0, n, circle));
   printf ("Approximation of area under y = x^2 between 1 and 3 is%8.5f .\n\n",
                    area (1.0, 3.0, n, parabola));
   return 0;
}

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

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

/* Finding area via the Trapezoidal Rule */
double area (double a, double b, int numInt, double f (double))
{  
  double width = (b - a) / numInt; 
  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;
}