ALGORITHM OF SIMPSON 3/8 RULE

ALGORITHM OF SIMPSON 3/8 RULE

1-Enter value of upper limit (a) and lower limit(b)

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)

   if (j % 3 = = 0)

   s = s+2*y(a+j*h)

   else

   s= s +3*y(a+j*h)

6- result = 3*(h/8) * s

7-Print result

8-exit ( )

PROGRAM FOR SIMPSON 3/8 RULE

/*PROGRAM FOR SIMPSON 3/8 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);

if(n%3==0)

{

h=(xf-x0)/n;

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

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

{

if(i%3==0)

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

else

y=y+3*f(x0+i*h);

}

y=(3*(y*h))/8;

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

}

else

goto X;

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::1.357081 */

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 */