0.000000 0.000000 0.000000
0.100000 0.099833 0.091123
.....................
.....................

1.500000 0.730990 0.712344
1.600000 0.862848 0.793431
1.700000 1.036497 1.012222
1.800000 1.257597 1.257597
1.900000 1.532184 1.532184
2.000000 1.866667 1.866667

plot "data.txt" using 1:2, title "Euler", "data.txt" using 1:3 title "Exact"

/* Simpson's rule */
#include <stdio.h>
#include  <math.h>

double f(double x)
 {return 4.0/(1.0+x*x);}

int main()
{
 int i, n ;
 double a=0.0, b=1.0 , h, s1=0.0, s2=0.0, s3=0.0, x;

 printf("Enter number of partitions (must be even) = ");
 scanf("%d", &n) ;

  h = (b-a)/(2.0*n) ;

  s1 = (f(a)+ f(b));

 for (i=1; i<2*n; i=i+2) s2 = s2 + f(a + i*h);

 for (i=2; i<2*n; i=i+2) s3 = s3 + f(a + i*h);

    printf("%f\n", (h/3.0)*(s1+ 4.0*s2 + 2.0*s3)) ;
 return 0;
}