Programming for Trapizoidal rule

/*trapizoidal rule*/

#include<stdio.h>

#include<math.h>

float fun(float x)

{

                float d;

                d=sqrt(1-(x*x));

                return(d);

}

void

main()

{

                float a,b,sum=0.0,integral=1.0,c=0.0,h;

                int i,n;

                printf("enter the lower and upper limits:");

                scanf("%f%f",&a,&b);

                printf("enter the total number of intervals:");

                scanf("%d",&n);

label:

                c=integral;

                h=(b-a)/n;

                sum=fun(a)+fun(b);

                for(i=1;i<n;i++)

                {

                                sum=sum+(2*fun(a+(i*h)));

                }

                integral=(h*0.5)*sum;

                if(fabs((integral-c)/integral)>0.001)

                {

                                n=n+10;

                                goto label;

                }

                printf("the value of the integral is %f and is converged for %d intervals",integral,n);

}

Result:

enter the lower and upper limits:0 1

enter the total number of intervals:10

the value of the integral is 0.784237 and is converged for 40 intervals

Press any key to continue

/*trapizoidal rule*/

#include<stdio.h>

#include<math.h>

float fun(float x)

{

                float d;

                d=(x*cos(x));

                return(d);

}

void

main()

{

                float a,b,sum=0.0,integral=1.0,c=0.0,h;

                int i,n;

                printf("enter the lower and upper limits in degree:");

                scanf("%f%f",&a,&b);

                printf("enter the total number of intervals:");

                scanf("%d",&n);

                a=a*(3.1415/180);

                b=b*(3.1415/180);

label:

                c=integral;

                h=(b-a)/n;

                sum=fun(a)+fun(b);

                for(i=1;i<n;i++)

                {

                                sum=sum+(2*fun(a+(i*h)));

                }

                integral=(h*0.5)*sum;

                if(fabs((integral-c)/integral)>0.001)

                {

                                n=n+10;

                                goto label;

                }

                printf("the value of the integral is %f and is converged for %d intervals",integral,n);

}

Result:

enter the lower and upper limits in degree:90 180

enter the total number of intervals:10

the value of the integral is -2.570212 and is converged for 20 intervals

Press any key to continue