Integrate a function using numerically using trapezoidal Method.

 

Numerical Integration Using Trapezoidal Method Algorithm

In numerical analysis, Trapezoidal method is a technique for evaluating definite integral. This method is also known as Trapezoidal rule or Trapezium rule.

This method is based on Newton's Cote Quadrature Formula and Trapezoidal rule is obtained when we put value of n = 1 in this formula. In this article, we are going to develop an algorithm for Trapezoidal method.

 

Trapezoidal Method Algorithm

1. Start

2. Define function f(x)

3. Read lower limit of integration, upper limit of  integration and number of sub interval

4. Calculate: step size = (upper limit - lower limit)/number of sub interval

5. Set: integration value = f(lower limit) + f(upper limit)

6. Set: i = 1

7. If i > number of sub interval then goto

8. Calculate: k = lower limit + i * h

9. Calculate: Integration value = Integration Value + 2* f(k)

10. Increment i by 1 i.e. i = i+1 and go to step 7

11. Calculate: Integration value = Integration value * step size/2

12. Display Integration value as required answer

13. Stop

 

Numerical Integration Using Trapezoidal Method C Program

 

C program for Trapezoidal Rule or Method to find numerical integration. To learn algorithm about Trapezoidal rule follow article Trapezoidal Method Algorithm.

 

#include<stdio.h>

#include<conio.h>

#include<math.h>

 

/* Define function here */

#define f(x) 1/(1+pow(x,2))

 

int main()

{

 float lower, upper, integration=0.0, stepSize, k;

 int i, subInterval;

 clrscr();

 /* Input */

 printf("Enter lower limit of integration: ");

 scanf("%f", &lower);

 printf("Enter upper limit of integration: ");

 scanf("%f", &upper);

 printf("Enter number of sub intervals: ");

 scanf("%d", &subInterval);

 /* Calculation */

 /* Finding step size */

 stepSize = (upper - lower)/subInterval;

 /* Finding Integration Value */

 integration = f(lower) + f(upper);

 for(i=1; i<= subInterval-1; i++)

 {

  k = lower + i*stepSize;

  integration = integration + 2 * f(k);

 }

 integration = integration * stepSize/2;

 printf("\nRequired value of integration is: %.3f", integration);

 getch();

 return 0;

}

 

 

Trapezoidal Method C Program Output

 

Enter lower limit of integration: 0

Enter upper limit of integration: 1

Enter number of sub intervals: 6

 

Required value of integration is: 0.784

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