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Re: Mathematica and Maple disagree on this integral

  • To: mathgroup at
  • Subject: [mg33252] Re: Mathematica and Maple disagree on this integral
  • From: "John Doty" <jpd at>
  • Date: Tue, 12 Mar 2002 05:08:38 -0500 (EST)
  • Organization: Wampler-Doty Family
  • References: <> <a61vd9$gqb$> <a6cia0$eio$>
  • Sender: owner-wri-mathgroup at

In article <a6cia0$eio$1 at>, "Ben Crain"
<bcrain at> wrote:

> Thanks for the clarification.  I have learned about the "principal
> value" integral, but did not know that one must distinguish between
> various definitions of the integral in Mathematica (or in Maple).  I
> think the "default" integral should be the most general, or most useful,
> definition of "integral".  Clearly
> (in my opinion) the most useful definition of "integral" would be (at
> least) the
> "principal value" integral;  so if you ask for Mathematica's integral of
> this function, what it returns is correct (i.e., most useful).  My
> standard for judgment is very practical:  suppose you had a model for a
> real-word process
> (e.g., designing an engine for a rocket), which required the evaluation
> of this integral.  Would you reject the design because the integral is,
> according to some definition, "divergent", or would you simply set the
> integral to zero, and accept the model. I think almost all engineers
> would accept the model  (assuming that is the only possible problem),
> and I am certain that the engine would work
> (assuming everthing else in the engine's design is correct).  That means
> that the "principal value" integral really is the "correct" answer.
> Other integrals are simply wrong!

The principal value is not always the correct solution to a physics or
engineering problem. It depends on what mathematical idealization produces
the singularity and why you find yourself attempting to integrate through
it. Sometimes the correct solution is to take a path around the
singularity in the complex plane.

| John Doty		"You can't confuse me, that's my job."
| Home: jpd at
| Work: jpd at

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