Trapezoidal

Program:

#include

#include

#include

#define f(x) sqrt(sin(x))

#define pi 3.1415926

#include

void main()

{

clrscr();

float a,b,h, fa, fb, I,fx[10];

float sum=0.0,sum1=0.0,sum2=0.0,fn;

char k;

int c,n,i;

a=0;

b=pi/2;

fa=f(a);

fb=f(b);

do{

clrscr();

printf("\n 1) Trapezoidal\n 2) Comp.Trapezoidal\n 3) Simpson's 1/3\n 4) Comp.simpson's 1/3\n 5) Simpson's 3/8\n 6) Boole's\n 7) Comparison Table");

printf("\nENTER YOUR CHIOICE:");

scanf("%d",&c);

switch(c)

{

case 1:

printf("\n\tTrapizoidal");

h=b-a;

I=h*((fa+fb)/2);

printf("\n\tThe result is %.4f",I);

break;

case 2:

printf("\n\tComposite trapezoidal:");

printf("\n\tEnter n:");

scanf("%d",&n);

h=(b-a)/n;

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

{

fx[i]=f(a+i*h);

sum=sum+fx[i];

}

fn=f(a+n*h);

I=(h/2)*(fa+2*sum+fn);

printf("\n\tThe result is: %.4f",I);

break;

case 3:

printf("\n\tSimpson's 1/3");

h=(b-a)/2;

fx[1]=f(a+h);

I=(h/3)*(fa+4*fx[1]+fb);

printf("\n\tThe result is: %.4f",I);

break;

case 4:

printf("\n\tComposite Simpson's 1/3:");

printf("\n\t Enter n:");

scanf("%d",&n);

h=(b-a)/n;

for(i=1;i<=(n/2);i++)

{

 fx[i]=f(a+(2*i-1)*h);

 sum1=sum1+fx[i];

 }

for(i=1;i<=((n/2)-1);i++)

{

fx[i]=f(a+2*i*h);

sum2=sum2+fx[i];

}

I=(h/3)*(fa+4*sum1+2*sum2+fb);

printf("\n\tThe result is: %.4f",I);

break;

case 5:

printf("\n\tSimpson's 3/8");

h=(b-a)/3;

for(i=1;i<=2;i++)

{

fx[i]=f(a+i*h);

sum=sum+fx[i];

}

I=(3*h/8)*(fa+3*sum+fb);

printf("\n\tThe result is: %.4f",I);

break;

case 6:

printf("\n\tBoole's Rule:");

h=(b-a)/4;

for(i=1;i<=3;i++)

{

fx[i]=f(a+i*h);

}

I=(2*h/45)*(7*fa+32*fx[1]+12*fx[2]+32*fx[3]+7*fb);

printf("\n\tThe result is: %.4f",I);

break;

case 7:

printf("\n\t RULE \t n\t RESULT");

printf(“\n\t----------------------------“);

printf("\n\t TRAPEZOIDAL\t 1\t0.78540");

printf("\n\t COMP. TRAPEZOIDAL\t 2\t1.05314");

printf("\n\t SIMPSON's 1/3\t 2\t1.14238");

printf("\n\t COMP. SIMPSON's 1/3\t 4\t1.17823");

printf("\n\t SIMPSON's 3/8\t 3\t1.16104");

printf("\n\t BOOLE's RULE\t 4\t1.18062");

break;

default:

exit(0);

}

printf("\n\t Continue??[y/n]");

k=getch();

}

while(k=='y'||k=='Y');

getch();

}