Re: Mathematica and Maple disagree on this integral

*To*: mathgroup at smc.vnet.net*Subject*: [mg33252] Re: Mathematica and Maple disagree on this integral*From*: "John Doty" <jpd at w-d.org>*Date*: Tue, 12 Mar 2002 05:08:38 -0500 (EST)*Organization*: Wampler-Doty Family*References*: <200203011152.GAA27858@smc.vnet.net> <a61vd9$gqb$1@smc.vnet.net> <a6cia0$eio$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

In article <a6cia0$eio$1 at smc.vnet.net>, "Ben Crain" <bcrain at bellatlantic.net> 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 w-d.org | Work: jpd at space.mit.edu

**References**:**Mathematica and Maple disagree on this integral***From:*Ben Crain <bcrain@bellatlantic.net>

**RE: how to rotate text in 2-D graphics?**

**Re: how to rotate text in 2-D graphics?**

**Re: Mathematica and Maple disagree on this integral**

**MathLink and List**