Finding area of regions: Trapizoid and Simpson method

by **bit0223-sujon** Sat May 07, 2011 8:14 pm

Hey guys, I am giving the C code of Trapizoid rule and Simpson's 1/3 rule. By these two methods we can get the result of a definite integration, or, in other words, we can say- we can find the area of a region very easily. I hope this will be helpful to everyone.

Code:: #include<stdio.h> #include<stdlib.h> #define f(x) (x)*(x) double trapizoid(double,double,double); double simpsons(double,double,double); int main(void){ double a,b,n,m,I,T,h,x,diff; int i; double sum1,sum2=0,sum3=0; printf("Enter a,b & m::"); scanf("%lf%lf%lf",&a,&b,&m); sum1=f(a)+f(b); n=2*m; I=simpsons(a,b,n); T=trapizoid(a,b,n); diff=fabs(T-I); printf("%Trapizoid=%lf\nSimpsons=%lf\n\ndifference=%18.10e",T,I,diff); return 0; } double simpsons(double a, double b, double n){ int i; double x,h,sum1,sum2=0,sum3=0; h=(b-a)/n; sum1=f(a)+f(b); printf("in simps h=%lf\n",h); for(i=1;i<=n/2-1;i++){ x=a+2*i*h; sum2+=f(x); } for(i=1;i<=n/2;i++) { x=a+(2*i-1)*h; sum3+=f(x); } return (h/3.0)*(sum1+2.0*sum2+4.0*sum3); } double trapizoid(double a,double b,double n){ int i; double x,h,sum=0; h=(b-a)/n; printf("in trapizoid h=%lf\n",h); for(i=1;i<=n-1;i++){ x=a+i*h; sum+=f(x); } sum=(h/2.0)*(f(a)+f(b)+2*sum); return sum; }