#include <stdio.h>        /* Header for input/output subroutines. */
#include <math.h>         /* Header for math subroutines. */
#include <float.h>        /* Header for floating point subroutines. */

#define pi 3.141592653589793238462643383279     /* Accurate value for pi. */

/* Simpson's rule for approximating integrals.
	a:              left endpoint
	b:              right endpoint
	fc:             pointer to function to integrate
	n:              number of subintervals
*/
double fc (double x);

main()
{
double a,b,h,sum,x,y;     /* In 'C' all variables must be assigned */
double p1, p2, p3;
int i, n;
printf("\007");           /* Sound bell in computer. */
a = (double) 0.0;
printf("\nLeft end point    = %.16lf",a);
b = (double) pi/2.0;
printf("\nRight end point   = %.16lf",b);
i = -1;
while (i < 0){
printf("\nEnter number of subintervals (must be even) ");
scanf("%d",&n);
i = n/2; i = 2*i - n;   /* Don't allow odd values of n.  */
if (n<=0) i = -1;       /* Don't allow zero or negative. */
}
printf("\nNumber of subintervals %d",n);
h = (double) (b-a)/n;
for (i=1, sum=0.0; i<=n; i = i+ 2){
  p1 = fc((double) a+(i-1)*h);
  p2 = fc((double) a+i*h);
  p3 = fc((double) a+(i+1)*h);
  sum += p1 + 4.0 * p2 + p3;
/* printf("\n x, f(x) %.16lf %.16lf",a+(i-1)*h,p1); */
/* printf("\n x, f(x) %.16lf %.16lf",a+i*h,p2);     */
/* printf("\n x, f(x) %.16lf %.16lf",a+(i+1)*h,p3); */
}

printf("\nValue of sum      = %.16lf", (double) sum);
y = (double) h*sum/3.0;
printf("\nValue of integral = %.16lf", (double) y);
/* x=(double) 2.0;
printf("\nTheoretical Value = %.16lf", (double) log((double) x));
printf("\n"); */
return(0);
}

double fc (double x)
{
    double y;
    y = (double) sqrt(1.0-sin(exp(1)/2.)*sin(exp(1)/2)*sin(x)*sin(x));
    return (y);
}

/* End of file */