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Integral Programming need help

Posted on 1999-07-23
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Last Modified: 2012-05-04
I need to solve this

phi = integral(0 - infinity) lnR(v)^1/2
                              --------------  dv
                              v0^2-v^2



I have this so far
NumMethods.h:

/* This file contains the declerations for Nummethods.

_--------------------------------------------------------------*/

typedef double (*FunctionPtr)(double);

double RectangleMethod(
            FunctionPtr FPtr,
            double a,
            double b,
            int n);
            
            
NumMethods.cpp :
/*this file contains the definition of some numerical methods.

...
------------------------------------------------------------------*/
#include "NumMethods.h"

/*------------------------------------------------------------------
Rectangle Method approximates the defintie integral of a function using the rectangle method with altitudes at the idpoints of the subintervals.
--------------------------------------------------------------------*/


double RectangleMethod(FunctionPtr FPtr,double Left, double Right, int n)
{                                    
double
      DeltaX = (Right - Left) / n,
      MidPt = Left + DeltaX / 2.0,
      Sum = 0.0;
      
      for (int i = 1; i <=n; i++)
      
       {
       Sum += FPtr(MidPt);
       MidPt += DeltaX;
       }
      
       return Sum * DeltaX;
      
       }

Calculus.cpp :
#include <math.h>
#include <iostream.h>
double F(double x)
{

return x * x +1 ;

}
//=================================================================



#include "NumMethods.h"

int main(void)
{
      cout<< "\nThis program approxximates the definated integral of a"
                  "\n\tfunction using the rectangle method.\n";
      int
            n;
            
      double
            a,
            b,
            ApproximateInt;
            
      char
            Answer;
            
      do
      {
            do
            {
                  cout<< "\nEnter the endpoints (a & b) of the integral: ";
                  cin >> a >> b;
                  }
            while ( a >= b);
            
            do
            {
                  cout<< "Enter the number of rectangles to be used: ";
                  cin>>n;
                  
                  ApproximateInt = RectangleMethod(F, a, b, n);
                  
                  cout << "--> An Approximation to the integral using"
                         << n << " recatangles is " << ApproximateInt << "\n\n";
                         
                         
                  cout << "\nChange the number of rectangles (y or n)? ";
                  cin >> Answer;
                  }
                  while ((Answer == 'y')  || (Answer == 'Y'));
                  
                  cout << "\nchange the starting interval (y or n)? ";
                  cin>> Answer ;
                  }
                  while ((Answer == 'y') || (Answer == 'Y'));
                  
                  return 0;
                  
                  
                  }
                  
This solve for a simple integral function of x^2 + 1
0
Comment
Question by:kimbola
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5 Comments
 
LVL 84

Expert Comment

by:ozo
ID: 1200902
Have you tried changing F to your function?
Are you having problems hear v=v0?
0
 
LVL 14

Accepted Solution

by:
AlexVirochovsky earned 400 total points
ID: 1200903
You must simple change  you
double F(double x)
{
 if (v0 != x)
   return sqrt(ln(x))/(v0*v0 - x*x);
return 0;//for example

}
and in you main programm must be something as
double v0;
cout << "\n Input v0 ";
cin >> v0;
Good Luck, Alex


0
 

Author Comment

by:kimbola
ID: 1200904
the thing is that R(v) is a sixth degree polynomial and must be solved first.  In other words R(v) and v are not the same variable.
0
 
LVL 84

Expert Comment

by:ozo
ID: 1200905
If your problem is in solving R(v), we may be better able to help you if you'd let us know what difficulty you're having.

0
 
LVL 14

Expert Comment

by:AlexVirochovsky
ID: 1200906
I agree with ozo, but from text of Q i uderstand(and mistake) , that
F = ln(v)^1/2
    --------------  
    v0^2-v^2
What is true definition?
 
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