/*************************************************************
* Program to demonstrate integration of a real function F(x) *
*                    by Simpson's method                     *
* ---------------------------------------------------------- *
* REFERENCE: "Mathematiques en Turbo-Pascal (Part 1) By      *
*             Marc Ducamp and Alain Reverchon, Eyrolles,     *
*             Paris, 1987" [BIBLI 03].                       *
* ---------------------------------------------------------- *
* SAMPLE RUN:                                                *
* (Integrate sin(x) from x=0 to x=1)                         *
*                                                            *
* Integral of a function F(X) by Simpson's method            *
*                                                            *
* Input begin and end values for x variable:                 *
*                                                            *
*         X0 = 0                                             *
*         X1 = 1                                             *
*                                                            *
* Number of integration steps: 100                           *
*                                                            *
*                                                            *
* Value of integral:  0.459698                               *
*                                                            *
*                                                            *
*                                C++ version by J-P Moreau.  *
*                                     (www.jpmoreau.fr)      *
*************************************************************/
#include <stdio.h>
#include <math.h>

double  x0,       //begin x value
        x1;       //end   x value
int     nstep;    //number of integration steps
double  result;   //result of integral


  // Given function to integrate
double FUNC(double x) {
  return sin(x);  
}


  /******************************************************
  * Integral of a function FUNC(X) by Simpson's method  *
  * --------------------------------------------------- *
  * INPUTS:                                             *
  *          a      begin value of x variable           *
  *          b      end value of x variable             *
  *          n      number of integration steps         *
  *                                                     *
  * OUTPUT:                                             *
  *          res    the integral of FUNC(X) from a to b *
  *                                                     *
  ******************************************************/
  void Integral_Simpson(double a, double b, int n, double *res) {
    int i; double step,r;
    step=(b-a)/2/n;
    r=FUNC(a);
    *res=(r+FUNC(b))/2;
    for (i=1; i<2*n; i++) {
      r=FUNC(a+i*step);
      if ((i%2) != 0) *res += r+r;
      else *res += r;
    }
    *res *= step*2/3;
  }

          
void main()  {
  printf("\n Integral of a function F(X) by Simpson's method\n\n");
  printf(" Input begin and end values for x variable:\n\n");
  printf("         X0 = "); scanf("%lf", &x0);
  printf("         X1 = "); scanf("%lf", &x1);
  printf("\n Number of integration steps: "); scanf("%d", &nstep);

  Integral_Simpson(x0,x1,nstep,&result);

  printf("\n\n Value of integral: %f\n\n", result);

}

// End of file tsimpson.cpp