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Subject: Re: Can I integrate the following function in MATLAB??
Date: Tue, 31 May 2011 05:19:04 +0000 (UTC)
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"kumar vishwajeet" wrote in message <is1pj2$15a$1@newscl01ah.mathworks.com>...
> I want to integrate the function in such a way that the result is still a function of a,b,c,d,e. I tried to do it using symbolic toolbox, but did not get any explicit solution. That's why I want to do it numerically.
- - - - - - - - - -
  I pose the question to you, Kumar.  Given that you cannot obtain a formula giving your double integral as an explicit function of the five parameters, what form would you expect a "numerical" solution to be in?

  When faced with just this problem for other functions, mathematicians, especially in the past, have used tables such as sine and cosine values as functions of their angles that were calculated numerically.  In more modern times, they have used computers with programs that could quickly carry out numerical computations necessary for their calculation.  Every time you call on 'exp', 'log', or 'atan2' you are calling on such programs.

  Now you are faced with a function of five different arguments, a, b, c, d, and e.  It would probably be quite impractical to produce tables with five independent variables like this.  If each variable were allowed to range over, say, a thousand different values to ensure good accuracy, your table would have to contain a thousand, million, million entries.

  So what is the next best thing you can do?  Of course.  Write yourself a matlab function with five arguments, which carries out the desired numerical double integration for whatever particular values of a, b, c, d, and e are entered.  This is the best you can hope to do in lieu of said monstrous tables or explicit formulas that no-one has ever discovered.  But that does mean that you must give up the idea of obtaining an answer in terms of five symbolic parameters!  Anyone who uses your function must specify all five arguments as definite numerical quantities.

Roger Stafford