Implementing Numerical Integration Using Function Pointers T

Implementing Numerical Integration Using Function Pointers The problem is to write a function \"integrate\" with prototype://FUNC represents functions of one variable that take a double as input and returns a double typedef double (*FUNC){double); double integrate(FUNC f, double a, double b); so that when it is passed a function f and bounds a and b, the call: integrate(f, a, b) will return the value of the definite integral of f evaluated between a and b. test integrate on the following three functions: double line(double x){return x; {double square(double x){return x*x; {double cube(double x){return x*x*x; {And the following main function: int main(){cout

Solution

#include <stdio.h>
#include <math.h>
#define PI 3.14159265

double f(double x);
double simpsons(int n, double a, double b);

int main()
{
double x0 = 0, xn = 10;
int i, n = 20;

for (i = 1; i <= 2; i++) {
n = i*20;
printf( \"For n=%d, the integral is %f\ \ \", n, simpsons(n, x0, xn));
n=n+20;
}
return 0;
}

double f(double x)
{
double y;

y = (x*exp(x))*pow(sin(0.5*PI*x),2);

return y;
}

double simpsons(int n, double a, double b)
{
int i;
double dx, x, sum;

dx = (b - a) / n;
sum = f(a) + f(b);
for (i = 1; i < n; i++) {
x = a + dx * i;
sum += 2 * (1 + i%2) * f(x);
}
sum *= dx/3;
return sum;
}