Integration Problem

This is a discussion on Integration Problem within the C Programming forums, part of the General Programming Boards category; Code: #include <stdio.h> #include <math.h> main() { double del_x, x, k, error, flag, f, sum, n_end; int n_trap, n1; printf("Part ...

  1. #1
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    Integration Problem

    Code:
    #include <stdio.h>
    #include <math.h>
    
    main()
    {
    
    double del_x, x, k, error, flag, f, sum, n_end;
    int n_trap, n1;
    
    printf("Part B:\n");
    printf("Integration of f(x) = sinh(x) on [-1,2]\n\n");
    
    do
    {
    printf("Enter the number of trapezoids:\n");
    scanf("%d", &n_trap);
    printf("n_trap = %d       del_x =%g\n", n_trap, 3./n_trap);
    n1 = n_trap +1;
    x = 0.0;
    f = sinh(x);
    sum -= 0.5 * f;
    for(k=0; k<n1; k++)
    {
    x = (double)k * (3./n_trap);
    f = sinh(x);
    sum += f;
    }
    
    sum -= 0.5 * f;
    sum *= (3./n_trap);
    printf("Integral = %g\n", sum);
    error = 100*((cosh(2)-cosh(1)) - sum);
    printf("Relative Error = %g percent\n\n", error);
    printf("Do you want new n_trap: y=1/n=0\n");
    scanf("%d", &flag);
    sum = 0;
    }while (flag ==1);
    }
    Sorry this one's so long. What I'm trying to do is integrate sinh(x) over the domain [-1, 2]. I SHOULD get that the Integral is 2.235734 when using TEN trapezoids, but instead I get this output.

    Code:
    Part B:
    Integration of f(x) = sinh(x) on [-1,2]
    
    Enter the number of trapezoids:
    10
    n_trap = 10       del_x =0.3
    Integral = -6.73572e+306
    Relative Error = Inf percent
    
    Do you want new n_trap: y=1/n=0
    Someone PLEASE help me. I've been working on this for hours, and I still can't get it.

  2. #2
    and the hat of int overfl Salem's Avatar
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    Code:
    $ gcc -W -Wall -ansi -pedantic -O2 foo.c
    foo.c:5: warning: return type defaults to `int'
    foo.c: In function `main':
    foo.c:35: warning: int format, double arg (arg 2)
    foo.c:7: warning: unused variable `del_x'
    foo.c:7: warning: unused variable `n_end'
    foo.c:38: warning: control reaches end of non-void function
    foo.c:7: warning: 'sum' might be used uninitialized in this function
    Pay attention to the 'sum' and 'printf' related messages.
    If you dance barefoot on the broken glass of undefined behaviour, you've got to expect the occasional cut.
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  3. #3
    The Richness... Richie T's Avatar
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    You have a whole bunch of variables, some you don't use, all of
    which are uninitialised. Making some basic changes and
    improving layout gives the following:

    Code:
    #include <stdio.h>
    #include <math.h>
    
    int main(void)	/*main returns int*/
    {
    	/*initialise all of these*/
    
    	double del_x = 0.0, x = 0.0, k = 0.0, error = 0.0, flag = 0.0, f = 0.0, sum = 0.0, n_end = 0.0;
    	int n_trap = 0, n1 = 0;
    
    	printf("Part B:\n");
    	printf("Integration of f(x) = sinh(x) on [-1,2]\n\n");
    
    	do
    	{
    		printf("Enter the number of trapezoids:\n");
    		scanf("%d", &n_trap);
    
    		printf("n_trap = %d       del_x =%g\n", n_trap, 3.0/n_trap);
    
    		n1 = n_trap +1;
    		x = 0.0;
    		f = sinh(x);
    		sum -= 0.5 * f;
    
    		for(k=0; k<n1; k++)
    		{
    			x = (double)k * (3./n_trap);
    			f = sinh(x);
    			sum += f;
    		}
    
    		sum -= 0.5 * f;
    		sum *= (3./n_trap);
    
    		printf("Integral = %g\n", sum);
    
    		error = 100*((cosh(2)-cosh(1)) - sum);
    
    		printf("Relative Error = %g percent\n\n", error);
    
    		printf("Do you want new n_trap: y=1/n=0\n");
    		scanf("%d", &flag);
    
    		sum = 0;
    	}while (flag == 1);
    
    	return 0;
    }
    This is given much more realistic answers but it is still not correct.
    You are implementing the formula incorrectly, and who taught you
    how to calculate percentage error? Generally its like this

    Percentage error = ((absolute value(Actual - approx))/Actual) * 100

    That should set you off in the correct direction. Look at the
    trapezoidal formula again.
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  4. #4
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    Yeah, it ain't working. My teacher insists the integral is correct, but I don't believe him. The integral looks correct, but maybe I'm not seeing something?

  5. #5
    The Richness... Richie T's Avatar
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    I could write code that did this correctly and explain it to you,
    but you wouldn't benefit as much from that as what I'm about to
    suggest - I googled for "trapezoidal rule" and this was the first
    link that popped up - it explains each term in the equation.

    My advice is to compare the formula to your approach, and if
    it is mostly incorrect (i didn't check that it is, but it probably is),
    scrap your current implementation and rewrite as close to the
    formula as possible - this can be done using a for loop that
    iterates for "the number trapezoids" times - a single statement
    can evaluate the result for each trapezoid. Use sensible variable
    names and the implementation should be easier to write.
    No No's:
    fflush (stdin); gets (); void main ();


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  6. #6
    and the hat of int overfl Salem's Avatar
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    So start learning how to debug your own code.
    Code:
    		for(k=0; k<n1; k++)
    		{
    			x = (double)k * (3./n_trap);
    			f = sinh(x);
    			sum += f;
    			printf( "Loop %f: x=%f, f=%f, sum=%f\n", k, x, f, sum );
    		}
    Does this output look OK, compared to what you worked out by hand?
    If it does, move on to your next calculations.

    Why is 'k' a floating point number, when used as a loop variable?
    If you dance barefoot on the broken glass of undefined behaviour, you've got to expect the occasional cut.
    If at first you don't succeed, try writing your phone number on the exam paper.
    I support http://www.ukip.org/ as the first necessary step to a free Europe.

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