Question

Paragraph Styles Voce Sraut Simpson's 1/3rd rule is an extension of Trapezoidal rule where the integrand is approximated by a second order polynomial instead of a first order polynomial. For a given function f(x) the integral of f(x) over an interval [a, b] using Simpson's 1/3rd rule is given by: S f(x)dx = odx =“ $(x)+4 ()+2 Ž f(x)+F(*,) a 1=1,3,5.... 1=2,4,6,... Where, n is the number of subintervals and h is the width of each subinterval. Write a complete C language program that implements Simpson's 1/3rd rule to approximate the 7.5 x? cos(x)+ xº sin(x)d« (assume n= 100). following integral:

Answer 1

`Hey,

Note: If you have any queries related to the answer please do comment. I would be very happy to resolve all your queries.

#include <stdio.h>
#include<math.h>
float func(float x)
{
return x*x*cos(x)+x*x*x*sin(x);
}
  
// Function for approximate integral
float simpsons_(float ll, float ul, int n)
{
// Calculating the value of h
float h = (ul - ll) / n;
  
// Array for storing value of x and f(x)
float x[1000], fx[1000];
int i;
// Calculating values of x and f(x)
for (i = 0; i <= n; i++) {
x[i] = ll + i * h;
fx[i] = func(x[i]);
}
// Calculating result
float res = 0;
for (i = 0; i <= n; i++) {
if (i == 0 || i == n)
res += fx[i];
else if (i % 2 != 0)
res += 4 * fx[i];
else
res += 2 * fx[i];
}
res = res * (h / 3);
return res;
}
  
// Driver program
int main()
{
float lower_limit = 0; // Lower limit
float upper_limit = 7.5; // Upper limit
int n = 100; // Number of interval
printf("Integration is %f\n",simpsons_(lower_limit,upper_limit,n));
return 0;
}

main.c 3 float func(float x) 4-{ 5 return x x*co (x) ** x*si (x); 63 7 8 // Function for approximate integral 9 float simpsons_(float ll, float ul, int n) 10- { 11 // Calculating the value of n 12 float h = (ul - 11) /n; 13 14 // Array for storing value of x and f(x) 15 float x[1000], fx[1000]; 16 int i; 17 // Calculating values of x and f(x) 18. for (i = 0; i <= n; i++) { 19 x[i] = 11 + i * h; 20 fx[i] = func(x[i]); 21 } 22 // Calculating result 23 float res = 0; 24 - for (i 0; i <= n; i++) { if G < 25. input Integration is 78.107368

Kindly revert for any queries

Thanks.