Write a computer code to implement the Composite Trapezoidal

Write a computer code to implement the Composite Trapezoidal Rule quadrature T_h[f] = h(1/2 f(x_0) + f(x_1) + ... + f(x_N-1) + 1/2 f(x_n)), to approximate the definite integral I|f| = integral^b_a f(x) dx, using the equally spaced points x_0 = a, x_1 = x_0 + h, x_2 = x_0 + 2h, ..., x_N= b, where h = (b-a)/N. Make sure that all your codes have a preamble which describes the purpose of the code, all the input variables, the expected output, your name, and the date of the last time you modified the code.

Solution

Below is the Code for Trapezoidal rule in C Programming.

#include<stdio.h>
#include<conio.h>
#include<math.h>
void main()
{
float x[10],y[10],sum=0,h,temp;
int i,n,j,k=0;
float fact(int);
clrscr();
printf(\"\ how many record you will be enter: \");
scanf(\"%d\",&n);
for(i=0; i<n; i++)
{
printf(\"\ \ enter the value of x%d: \",i);
scanf(\"%f\",&x[i]);
printf(\"\ \ enter the value of f(x%d): \",i);
scanf(\"%f\",&y[i]);
}
h=x[1]-x[0];
n=n-1;
for(i=0;i<n;i++)
{
if(k==0)
{
sum = sum + y[i];
k=1;
}
else
sum = sum + 2 * y[i];
}
sum = sum + y[i];
sum = sum * (h/2);
printf(\"\ \ I = %f \",sum);
getch();
}