Question

nt y y- fox) (xo Yo) Figure 5.26 Approximating the Area Under a Curve with Trapezoids n-1 T(a)(ai) for n subintervals of length h Write a function trap with input parameters a, b , and f that implements the trapezoidal rule. Call trap with values for n of 2, 4, 8, 16, 32 64, and 128 on functions g (x)sinz (a - 0,b 3.14159) and h (x)- V4-z' (a2, b-2) Function h defines a half-circle of radius 2. Compare your approximation to the actual area of this half-circle Note: If you have studied calculus, you will observe that the trapezoidal rule is approximating f (z) dr

Original question is above, and is for C programming. As you will see in my code below, I am not sure how to properly implement the functions I made for g(x) and h(x) (I call them g_x and h_x) into my function called trap. I know that in my main function in my function call to trap, I have to put something in the parentheses of g_x() and h_x() since they both take a type double argument, however I'm not sure what to write since ultimately the arguments they take will actually come from the function trap

/*
Create a function "trap" with input parameters a, b, n, and f that implements the trapezoidal rule
to approximate the integral of f(x) from a to b. Call trap with values for n of 2, 4, 8, 16, 32, 64, 128
on functions g(x) = x^2sinxx (a = 0, b = PI) and h(x) = sqrt(4-x^2) (a = -2, b = 2)
*/

#include
#include
#define PI 3.14159
double g_x(double x);
double h_x(double x);
double trap(int n, double a, double b, double f(double));
int main(int argc, char *argv[]) {
   int n;
   printf("TRAPEZOIDAL RULE g(x) = x^2sin(x), a = 0, b = PI\n");
   for (n = 2; n <= 128; n *= 2)
   {
       printf("for n = %d, area is approximately %.4f\n", n, trap(n, 0, PI, g_x()));
   }
   printf("\n");
   printf("TRAPEZOIDAL RULE h(x) = sqrt(4 - x^2), a = -2, b = 2\n");
   for (n = 2; n <= 128; n *= 2)
   {
       printf("for n = %d, area is approximately %.4f\n", n, trap(n, -2, 2, h_x()));
   }
   return 0;
}

double trap(int n, double a, double b, double f(double))
{
   double h = (b - a) / n;
   double riemann_sum = 0;
   double area_approximation;
   double i;
   for (i = a + h; i <= b - h; i += h)
   {
       riemann_sum += f(i);
   }
   area_approximation = (h / 2) * (f(a) + f(b) + 2 * riemann_sum);
   return area_approximation;
}

double g_x(double x)
{
   return pow(x, 2) * sin(x);
}
double h_x(double x)
{
   return sqrt(4 - pow(x, 2));
}

Answer 1

THE PROBLEM IN YOUR CODE IS THAT WHEN YOU CALL THE METHOD TRAP, AND PASSING ANOTHER FUNCTION CALL AS PARAMETER WHICH WILL SIMPLY MEAN THAT FIRST THE FUNCTION g_x() OR h_x() WILL BE CALLED.

OR

ANOTHER METHOD CAN'T BE PASSED AS PARAMETER IN A METHOD AS THIS.

IN THIS CASE THE PARAMETER THAT WILL BE PASSED WILL BE THE RESULT OF THAT ANOTHER METHOD.

THUS, JUST PASS SOME char DATA WHICH WILL BE USED TO IDENTIFY WILL FUNCTION SHOULD BE CALLED AND USE IF-ELSE CONDITION.

THE CODE IS AS FOLLOWS-

#include<stdio.h>
#include<math.h>
#define PI 3.14159

double g_x(double x);
double h_x(double x);
double trap(int n, double a, double b, char F);

int main(int argc, char *argv[])
{
   int n;
    printf("TRAPEZOIDAL RULE g(x) = x^2sin(x), a = 0, b = PI\n");
    for (n = 2; n <= 128; n *= 2)
    {
   printf("for n = %d, area is approximately %.4f\n", n, trap(n, 0, PI, 'g'));
    }
    printf("\n");

    printf("TRAPEZOIDAL RULE h(x) = sqrt(4 - x^2), a = -2, b = 2\n");
    for (n = 2; n <= 128; n *= 2)
    {
    printf("for n = %d, area is approximately %.4f\n", n, trap(n, -2, 2, 'h'));
    }
    return 0;
}

double trap(int n, double a, double b, char F)
{
    double h = (b - a) / n;
    double riemann_sum = 0;
    double area_approximation;
    double i;
    if(F=='g')
    {
       for (i = a + h; i <= b - h; i += h)
        riemann_sum += g_x(i);
        area_approximation = (h / 2) * (g_x(a) + g_x(b) + 2 * riemann_sum);
        return area_approximation;
    }
   
   else
    {
        for (i = a + h; i <= b - h; i += h)
        riemann_sum += h_x(i);
        area_approximation = (h / 2) * (h_x(a) + h_x(b) + 2 * riemann_sum);
        return area_approximation;
    }
}

double g_x(double x)
{
return pow(x, 2) * sin(x);
}

double h_x(double x)
{
return sqrt(4 - pow(x, 2));
}