Thread: Trapezoidal Rule with a slight twist

Hi all! Here's the link the the prompt for the question i'm working on:

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and here is the code I have so far

// Chapter 5, #17
// This program will approximate the area
// under the curve/

Code:

#include <stdio.h>
#include <math.h>


double Trap (double A, double B, int N);


double G(double x);


double H (double a, double b, double n);


int main(void)


{


    double A, B, N;
    double Integral;




    printf("Please Enter the Values for A:"); scanf("%lf", &A);
    printf("\n");
    
    printf("Please Enter the Values for B:"); scanf("%lf", &B);
    printf("\n");
    
    printf("Please Enter the Values for N:"); scanf("%lf", &N);
    printf("\n");


    Integral = (H(A, B, N)/2.0) * Trap(G(A), G(B), N);
    
    printf("The approximate value of the area under this curve is:  " "%5.2f", Integral);
    printf("\n");
    printf("\n");
    
    
    
    return 0;
}


double Trap (double A, double B, int N)
{
    
    double i;
    double sum = 0.0;
    
    i = 1;
    while (i <= (N - 1.0))
    {
        sum = pow(i, 2) * sin(i)  ;
        
        i ++ ;
        
    }
    
    
    return (A + B + (2 * sum));


}


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


double H (double A, double B, double N)
{
    
    return (B-A)/N ;


}

So i'm having some trouble setting it up as well as with the prompt.


The prompt asks me to create a function Trap with a, b, n and F as inputs


However if I create a function F and call it for Trap then input a as F(a) and b as F(b) then why do I need F as an input for F?


Furthermore if I write F as a a parameter in F i assume I would write:

(A, B, N, (pow(a, 2)* sin(a)) + pow(b, 2)* sin(b)) so then why do I need inputs A and B in This case?

Also I'm sure there's something wrong with the way I actually wrote the sum of F(x), but can't figure it out yet. Will continue working on it for now,


Can anyone offer any advice? I would greatly appreciate it!!

Yeah H definitely doesn't need to be a function, but I saw no harm in it. I'll get rid of it for aesthetics.

What really confuses me is getting rid of the function G I made - If I remove, I think you're saying build under the code for Trap

so it would look like:

Code:

double Trap (double A, double B, int N)
{
    
    double i;
    double sum = 0.0;
    
    i = 1;
    while (i <= (N - 1.0))
    {
        sum = sum + pow(i, 2) * sin(i)  ;
        
        i = i +1 ;
        
    }
    
      G = 
    
    return (A + B + (2 * sum));


}

If it were me, I would write:

Code:

typedef double (*CurveFunction)(double);
double trap(double a, double b, int n, CurveFunction f);

Then you can call:

Code:

for (n = 2; n <= 128; n *= 2)
   printf("Approximate area under G curve (%d strips): %.03f \n", n, trap(0, 3.14159, n, &G));

for (n = 2; n <= 128; n *= 2) 
    printf("Approximate area under H curve (%d strips): %.03f \n", n, trap(-2.0, 2.0, n, &H));

This allows you more flexibility. Call f(x) under trap to get the y part of the graph no matter which curve it is.

Other than that I'm not sure how to integrate, I think you just sum the area of each strip which is by definition a trapezoid.

Huh, wow thanks for opening my eyes.

I think this will be really helpful.

Thank you very much!