ALGORITHM OF SIMPSON’S 1/3 RULE

ALGORITHM OF SIMPSON’S 1/3 RULE

1-Enter value of upper limit & lower limit

2-Enter value of sub-interval(n)

3-h=(b-a)/n

4-s=y(a)+y(b)

5-For (j=1 to n-1) dø

   if( j%2==0)

  {

   s= s+2*y(a+j*h)

  else

  s=s+4*y(a+j*h)
  }

6-Result = (h/3)*s

7-Print  “result”

8- exit( )

PROGRAM FOR SIMPSON 1/3 RULE

/*PROGRAM FOR SIMPSON 1/3 RULE*/

#include<stdio.h>

#include<conio.h>

void main()

{

int n,i;

float x0,xf,y,h;

float f(float);

clrscr();

printf("\n\nEnter the values of x0 & xf::");

scanf("%f%f",&x0,&xf);

printf("\n\nEnter the values of n::");

scanf("%d",&n);

h=(xf-x0)/n;

y=f(x0)+f(xf);

for(i=1;i<=n-1;i++)

{

y=y+2*f(x0+i*h);

}

y=y*h/2;

printf("\n\nThe result is::%f",y);

getch();

}

float f(float x)

{

return(1/(1+x*x));

}

/*************OUTPUT******************

 Enter the values of x0 & xf::0 6  

Enter the values of n::6

 The result is::1.410799 */