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MathGroup Archive 2007

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Re: Definite Integration in Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg74564] Re: Definite Integration in Mathematica
  • From: "Michael Weyrauch" <michael.weyrauch at gmx.de>
  • Date: Mon, 26 Mar 2007 02:08:35 -0500 (EST)
  • References: <etqo3f$10i$1@smc.vnet.net>

Hello,

   thanks, Dimitris, for bringing up this issue. (By the way, as I just realized, Michael Trott
in his book on symbolics has quite some interesting things to say related to this issue.)

My remark in this thread clearly was written in the spirit of "functions of one real 
variable". As I see my statements are clearly incorrect in the sense of  "functions of a complex
variable".

However, in many practical applications people want to have an integral in the
former sense, and it is very disconcerting to fall down a discontinuity step along
an integral of a continous integrand on the real line due to a singularity of the
integrand somewhere in the complex plane.  Therefore, I guess, the designers of "the other
CAS", which Dimitris uses for comparison, obviously opted to return an integral, which is continuous along
the real axis (if such an integral is available in the set of possible solutions).

This is not just a matter of aestetics or simplicity as Dimitris remark in this thread may suggest

>Do you prefer the extend antiderivative over the compact one obtained
>directly
>by Mathematica only because is real in the real axis?
>As regards myself, no!

In applications we have to use that solution which makes practical sense, and in many
applications it's the integral which is continouus (and differentiable) for a continouus integrand
on the real axis. Of course, it's my task as a physicist or engineer to see if a mathematical
solution serves my purposes or not, however, in such rather intriguing cases, it would be
desirable that  the designers of Mathematica would help me by providing an Option
to Integrate, in which I could ask for an integral which is continuous on the real axis if such an integral
exists for a particular integrand. 
(As I understand the remark of Daniel Lichtblau in some future version of Mathematica 
they may provide such an Option).

Thanks again

Michael Weyrauch


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