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Re: Re: Simple integral wrong

  • To: mathgroup at
  • Subject: [mg25114] Re: [mg25073] Re: Simple integral wrong
  • From: Andrzej Kozlowski <andrzej at>
  • Date: Sun, 10 Sep 2000 03:14:36 -0400 (EDT)
  • Sender: owner-wri-mathgroup at

on 00.9.8 11:28 AM, Paul Cally at cally at wrote:

> Or just type
> Integrate[Abs[Cos[u]],{u,0,Pi x}]
> Mathematica 4 returns
> 2
> Out[1]= Sqrt[Cos[Pi x] ] Tan[Pi x]
> (Actually, I don't think Mathematica 3 can do it at all.) This
> plots as a saw-tooth. The true solution should be
> Sqrt[Cos[Pi x]^2] Tan[Pi x] + 2 Floor[x + 1/2]
> Mathematica misses the step functions necessary to make the solution
> continuous.
> Thanks for your interest,
> Paul Cally

This is by no means "the true solution"! As is explained in countless books
and the online documentation (and also in my first posting) Mathematica
interprets Integrate[Abs[Cos[u]],{u,0,Pi x}] as a path integral in the
complex plane. The function Floor[x + 1/2] has no meaning  for complex x!
Moreover, it is quite wrong to think of Integrate[Abs[Cos[u]],{u,0,Pi x}] as
"indefinite integral". Note that

Integrate[Abs[Cos[u]], u]

Integrate[Abs[Cos[u]], u]

which shows that Mathematica does distinguish an "indefinite integral" from
a path integral.

Andrzej Kozlowski
Toyama International University, JAPAN

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