C Program for Gauss-Legendre Integration

//for integration of f(x) from a to b.

#include <stdio.h>

#include <conio.h>

#include <math.h>

void GaussLegendre(float,float,int);

float f(float x){return (exp(x));}

float g(float a,float b,float z)

{float x=(b-a)/2*z+(b+a)/2;

return (exp(x));}

void main()

{

float a,b;

int n;

printf("Enter a and b: ");

scanf("%f%f",&a,&b);

INPUT:

printf("Enter 2 for 2-point formula: \n");

printf("Enter 3 for 3-point formula: \n");

printf("Enter 4 for 4-point formula: \n");

scanf("%d",&n);

switch(n)

{

  case 2:

    printf("Using 2-point Formula::\n");

    GaussLegendre(a,b,n);

    break;

  case 3:

    printf("Using 3-point Formula::\n");

    GaussLegendre(a,b,n);

    break;

  case 4:

    printf("Using 4-point Formula::\n");

    GaussLegendre(a,b,n);
    break;
  default:
    printf("INVALID\n");
    goto INPUT;
}
getch();
}

void GaussLegendre(float a,float b,int n)
{
float I;
if(a==-1 && b==1)
{
  if(n==2)
  {
  I=1*f(-1/sqrt(3))+1*f(1/sqrt(3));
  printf("I=%f",I);
  }
  if(n==3)
  {
  I=5/9*f(-sqrt(3/5))+8/9*f(0)+5/9*f(sqrt(3/5));
  printf("I=%f",I);
  }
  if(n==4)
  {
I=0.34785*f(-0.86114)+0.65215*f(-0.33998)+0.65215*f(0.33998)+0.34785*f(0.86114);
  printf("I=%f",I);
  }
}
else
{
  if(n==2)
  {
  I=(b-a)/2*(1*g(a,b,-1/sqrt(3))+1*g(a,b,1/sqrt(3)));
  printf("I=%f",I);
  }
  if(n==3)
  {
I=(b-a)/2*(5/9*g(a,b,-sqrt(3/5))+8/9*g(a,b,0)+5/9*g(a,b,sqrt(3/5)));
  printf("I=%f",I);
  }
  if(n==4)
  {
I=(b-a)/2*(0.34785*g(a,b,-0.86114)+0.65215*g(a,b,-0.33998)+0.65215*g(a,b,0.33998)+0.34785*g(a,b,0.86114));
  printf("I=%f",I);
  }
}
}

OUTPUT:

For f(x)=exp(x) from -1 to 1

For f(x)=exp(x) from 0 to 1