Driver program

Cut and paste the main program below from the HTML version of this problem set. You should place your code for Problems 1.2 and 1.3 at the spot labelled ``YOUR ROUTINES GO HERE''.

The program below will drive your routines to compute the integral

$$\int_0^1 \frac{1}{\frac{1}{4}+\frac{\pi}{8}} \frac{1}{\left(1+x^2\right)^2} \, dx= 1.$$

/*
  Main program for PS#1
  Tests Simpson and Trapezoid integration routines
 */


/* Standard C header for using I/O and math libraries */
#include <stdio.h>
#include <math.h>

/* *** YOUR ROUTINES GO HERE *** */
                    .
                    .
                    .


/* Maximum size of N for integrations */
#define Nmx 200000
main()
{
  /* Declare space for arrays, remember that there are N+1 points! */
  /* Double precision for accurate numerical work... */
  double r[Nmx+1],dr[Nmx+1],f[Nmx+1];

  /* Declare working variables */
  int i,N;
  double u;

  /* Trick to get all digits of PI to the full machine precision */
  double pi;
  pi=4.*atan(1.);


  /* Loop over sizes 2, 20, 200, 2000, ..., Nmx */
  for (N=2; N<=Nmx; N*=10) {
    /* For each size, fill in arrays */
    for (i=0; i<=N; i++) {
      /* Let u be equally spaced between 0 and 1, -inclusive- */
      u=((double) i)/((double) N);

      /* Define change of variables */
      r[i]=u;
      dr[i]=1.;

      /* Specify function */
      f[i]=1/(1+r[i]*r[i])/(1+r[i]*r[i])/(0.25+0.125*pi);
    }

    /* Special cases at end points (reasons for this will become clear...) */
    f[0]=f[0];
    r[0]=r[0];
    dr[0]=dr[0];

    f[N]=f[N];
    r[N]=r[N];
    dr[N]=dr[N];

/* Call integration routines and output results... */
    printf("Trap, Simp: %7d %20.14f,%20.14f\n",N,trapint(f,r,dr,N),simpint(f,r,dr,N));
  }  

}