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MathGroup Archive 2005

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Re: Integrate vs Nintegrate for impulsive functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg61728] Re: Integrate vs Nintegrate for impulsive functions
  • From: Bill Rowe <readnewsciv at earthlink.net>
  • Date: Thu, 27 Oct 2005 05:02:05 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

On 10/26/05 at 2:44 AM, chris.chiasson at gmail.com (Chris Chiasson)
wrote:

>My computer gives the same answer as yours for NIntegrate, but it
>thought for a long while on Integrate and then spit out:
>Complex[-4.4073414839228176`*^145,6.238877585945074`*^146] Bug??
>Version Number: 5.2.0.0 
>Platform: Windows

Using version 5.2 on MacOS 10.4.2, for Integrate I get

Out[2]=
4.651767835491884*^136 + 1.162941958872971*^136*I

and for NItegrate, I get the same result reported by Pratik Desai.

The function being integrated is specified with machine precision coefficients. I strongly suspect this is the root of the problem.

Integrate will first get a symbolic answer then compute the final answer by substituting the end points into the symbolic answer. It is entirely possible this leads to problems even when the orginal function being integrated has reasonable values over the range of integration.

So, I would be inclined to accept the answer given by NIntegrate as valid and reject the answer given by Integrate. But I would not consider this to be a bug. Instead, I would chalk this up as one of the issues with doing machine precision computations.
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