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Re: Re: Simple integral wrong
*To*: mathgroup at smc.vnet.net
*Subject*: [mg25114] Re: [mg25073] Re: Simple integral wrong
*From*: Andrzej Kozlowski <andrzej at bekkoame.ne.jp>
*Date*: Sun, 10 Sep 2000 03:14:36 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
on 00.9.8 11:28 AM, Paul Cally at cally at kronos.maths.monash.edu.au 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
In[4]:=
Integrate[Abs[Cos[u]], u]
Out[4]=
Integrate[Abs[Cos[u]], u]
which shows that Mathematica does distinguish an "indefinite integral" from
a path integral.
--
Andrzej Kozlowski
Toyama International University, JAPAN
For Mathematica related links and resources try:
<http://www.sstreams.com/Mathematica/>
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