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Re: Problem finding integral of exponentials

  • To: mathgroup at smc.vnet.net
  • Subject: [mg59640] Re: Problem finding integral of exponentials
  • From: "James Gilmore" <james.gilmore at yale.edu>
  • Date: Mon, 15 Aug 2005 06:50:32 -0400 (EDT)
  • Organization: Yale University
  • References: <200508130726.DAA00918@smc.vnet.net> <ddn13u$cv5$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

Yes I have checked this on my version of Mathematica 5.0, and the integral
(Econt) cannot be expressed in any form. Since there is no clear
transformation to make on the argument, I think you will have to
numerically evaluate the integral for your given constants, or use
a series expansion in t to approximately determine the analytic behavior.

James Gilmore

"Kevin Towles" <kbt22 at drexel.edu> wrote in message 
news:ddn13u$cv5$1 at smc.vnet.net...
>
> I have a fairly specific problem of not being able to obtain the
> definte integral of a fairly complex function.  Does this mean that
> this integral is not possible in Mathematica?
>
> a = AverageDiameter;
> r0 = ForsterRadius;
> h = BilayerThickness;
> R = DomainDiameter;
> =CF=84 = DonorLifetime;
>
> ThisLayer = Integrate[(1 - Exp[(-(t/=CF=84))*(r0/r)^6])*2*Pi*r, 
> {r,a,TotalR}];
> OtherLayer = Integrate[(1 - Exp[(-(t/=CF=84))*(r0/r)^6])*2*Pi*r, {r, 
> h,TotalR}];
> pCont = Exp[-(t/=CF=84)]*Exp[(-=CF=83A)*(ThisLayer + OtherLayer)];
> Econt = 1 - (1/=CF=84)*Integrate[pCont, {t, 0, TotalTime}];
>
>
> All of the variable listed first (a, r0, h, R, and tau) are constants.
>
> Any help is appreciated,
>
> Kevin Towles
>
> 



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