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Re: Solving simultaneous integral equation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg100774] Re: Solving simultaneous integral equation
  • From: Bill Rowe <readnews at sbcglobal.net>
  • Date: Sat, 13 Jun 2009 06:05:26 -0400 (EDT)

On 6/11/09 at 9:45 PM, mat.davies at rolls-royce.com (Mat Davies) wrote:

>I have a problem of the form

>Integrate[f[s],{s,(b-e)/c,(b+e)/c]

>I am trying to solve for c and e (b is known). f[s] cannot be
>integrated algebraicly, only by by setting values for e and c and
>using NIntegrate.

>I also have a supplimentary equation linking b and c, which cannot
>be inverted using solve to give a relationship between e and c.

>I am trying to use NSolve or FindRoot to solve the system of
>equations, but I keep getting errors saying that algebraic limits
>are invalid for NIntegrate.

The obvious way to get around this particular error message
would be to use say x and y for the limits of integration then
solve for b and e using Solve or NSolve. That is, use FindRoot
with NIntegrate[f[s], {s, x, y}] to find suitable values for x
and y. Then b will be c(x+y)/2 and e will be c(y-x)/2.

However, I am not sure this will be all that useful. My guess is
there are an infinite number of pairs for any given f[s] that
will cause the definite integral to have a specific value. This
is clearly true for the simple f[s]:= 1 since the integral
becomes simply the difference between the integration limits.



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