Composite Trapezoidal Method

Algorithm : Composite Trapezoidal Rule
Composite_trapezoidal(a,b,n)
	{
Let us consider a function f(x). We want to find the integrating value of f(x)
w.r.t. x from lower limit ‘a’ to upper limit ‘b’ with subdivision n.

	h=(b-a)/n
	x=a
	for(i=1 to n-1)
		{
		    x=a+i*h
		    sum=sum+f(x)		//f(x) is a function which 
                 }				  returns the value of f(x)
	r=h/2*[f(a)+f(b)]+h*sum	                  at x=x
	print “r”
}						

C Program For Composite Trapezoidal Method

Source Code:

#include<stdio.h>
#include<conio.h>
#include<math.h>

void comp_trapezoidal(float,float,int);
float f(float);
void main()
{
 int n;
 float a,b;
 clrscr();
 printf("\nCALCULATE :\n");
 printf("\n%c\n%c(4x-3X^3)dx using the given limits.\n",244,245);
 printf("\nEnter the upper limit of the function:");
 scanf("%f",&b);
 printf("\nEnter the lower limit of the function:");
 scanf("%f",&a);
 printf("\nENTER THE NUMBER OF SUB-DIVISIONS:");
 scanf("%d",&n);
 comp_trapezoidal(a,b,n);
 getch();
}

void comp_trapezoidal(float a,float b,int n)
{
 float h,sum=0,x,R;
 int i;
 h=(b-a)/n;
 x=a;
 for(i=1;i<=n-1;i++)
 {
  x=a+i*h;
  sum=sum+f(x);
 }
 R=(h/2)*(f(a)+f(b))+h*sum;
 printf("\n\nValue=%f",R);
 }

float f(float x)
{
 return (4*x-3*x*x);
}



OUTPUT :

CALCULATE :

ô
õ(4x-3X^3)dx     using the given limits.

Enter the upper limit of the function:1

Enter the lower limit of the function:0

ENTER THE NUMBE3R OF SUB-DIVISIONS:10


Value=0.995000