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.