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Area under a curve

Posted on 1997-08-05
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Last Modified: 2008-02-26
Area of a region under the curve can be described by taking the integral of the function, given the limits of the curve. My problem is to write a program in C, using "Functions" to calculate the area of the region under the curve. The formula/equation to be used to solve is:
Area=Delta*[ {f(a)/2} + {f(a+delta)} + {f(a+2*delta)} + {f(a+3*delta)} + ............. + {f(a+(n-1)*delta)} + {f(b)/2} ] , where delta=((b-a)/n), a=(-1.0) and b=(1.0) and are REAL.
The equation of the curved line is given by:
y = e^ ((-x^2)/2)

Your quick response will be greatly appreciated. Thank you very much.

Sincerely,
Abdul
<batla@msn.com>
<batla@hotmail.com>
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Question by:batla
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Accepted Solution

by:
tomii earned 200 total points
ID: 1252876
I'm assuming that n is the number of points along the curve to take, or in other word, delta = 1-(-1)/n = 2/n....  I'm also assuming that Y=f(x)...  In this case, something like this may work...  (I haven't tested this, so there may be a bug or two)

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

double f(double);
double Area(int, double, double);

void main()
{
      int num_points = 100;

      printf("Area under the curve is: %lf", Area(num_points. -1.0, 1.0));
}
      

double f(double x)
{
      return(exp((-pow(x,2))/2.0));
}

double Area(int n, double start, double end)
{
      double area = 0.0;
      double delta = 0.0;
      long int count = 0;

      delta = (end - start) / n;

      area = f(start) / 2.0;
      area += f(end) / 2.0;

      for(i=start+delta ; i<end ; i+=delta)
      {
            count++;
            area += f(start + (count * delta));
      }

      return(area);
}
      
0
 

Author Comment

by:batla
ID: 1252877
Thanks Tomii. It was a good try but for some reason, it did not work at all. I fixed all the bugs and made it bug-free but it never returned any values to the main and as a result: there was not output. It seemed that it was stuck in some loop. You might wanna try to run it and if runs, e-mail me again. Thanks again for your efforts.

Abdul

0
 

Expert Comment

by:tomii
ID: 1252878
There were some bugs...  It has been mailed to you personally, to batla@msn.com
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