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Re: Integrating Abs[Sin[]^2]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg39096] Re: Integrating Abs[Sin[]^2]
  • From: Jos R Bergervoet <antispam at nospam.com>
  • Date: Wed, 29 Jan 2003 03:37:07 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

David W. Cantrell wrote:
> 
> "Dr Bob" <drbob at bigfoot.com> wrote:
> > Mathematica is NOT giving wrong answers in this case.
> >
> > It is assuming (non-zero) real parameters and giving the right
> > answer in that case.
> 
> Whether Mathematica is or is not giving a "wrong" answer in the case
> result = Integrate[ Abs[Sin[k x]]^2, {x,0,1}]; N[ result /. k->I+1 ]
> depends upon whether it is or is not appropriate for Mathematica to
> make a default assumption that k is a nonzero real. IMO, that could be
> debated.

It would be extremely silly to defend this as a "default assumption,"
since in all other cases Mathematica goes through a lot of trouble
to single out cases like "Im[k] == 0" in its answers.
 
> But surely, as I noted previously in this thread, Mathematica -- at
> least version 4.2 for Windows -- does give a wrong answer for
> result = Integrate[ Abs[Sin[k x]]^2, {x,0,1}, Assumptions->
> Element[k, Complexes]; N[ result /. k->I+1 ]. I do not see how the
> incorrectness of this can be debated (other than to say that
> Mathematica should be allowed to ignore an _explicitly stated_
> assumption!)

Coming to think of it, Mathematica could of course also ignore _any_
explicitly stated fact in its input and give the default result "42"
to all questions! But version 4.2 is probably still lacking one order
of magnitude in wisdom to do this. :-)

-- Jos  < Jos.Bergervoet@philips .n_o_spa_m. com >


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