CPNM LAB PROGRAM-14

 

14. Implement Gaussian quadrature for numerical integration .

           FLOW CHART :-

Algorithm:

Step – 1 : Start

Step – 2 : Declare p, q, r, a, b, k as float variables

Step – 3 : Enter limits a and b

Step – 4 : Assign p = (a + b) / 2

Step – 5 : Assign q = (b – a) / 2

Step – 6 : Assign Integral = q *(f(p + q / sqrt(3))+f(p-q/sqrt(3)))

Step – 7 : Print integral value

Step – 8 : Stop

Step – 1 : Call function float f(float x)

Step – 2 : return(x * x + 2 * x)

Program:

#include<stdio.h>

#include<conio.h>

#include<stdlib.h>

#include<math.h>

float f(float x)

{

//return(exp(-x*x));

return(x * x + 2 * x);

}

main()

{

float p, q, a, b, Integral;

clrscr();

printf("Enter a and b limits \n");

scanf("%f,%f",&a,&b);

p = (a + b) / 2;

q = (b - a) / 2;

Integral = q *(f(p + q / sqrt(3))+f(p-q/sqrt(3)));

printf("Integral = %f\n", Integral);

getch();

return 0;

}

Output:

Enter a and b limits

2, 4

Integral = 30.666666