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Topic: problems integrating a function
Replies: 5   Last Post: Jan 5, 2011 11:38 AM

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Walter Roberson

Posts: 7,673
Registered: 1/20/06
Re: problems integrating a function
Posted: Jan 5, 2011 10:46 AM
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On 04/01/11 7:29 PM, Marcio Barbalho wrote:
> Please,
> Could any of you find the numerical solution to the integral of
> sin[(x-pi)/sqrt(x)] from pi/100 to pi?
>
> S = int(sin((x-pi)/sqrt(x)),x=pi/100..pi)


I can't speak about MuPad (the current Matlab symbolic engine), but when
I investigate in Maple, I find that some of the avenues to creating the
integral involve (either implicitly or explicitly) summations of an
expression from 0 to infinity, and that depending on how the terms of
that expression are arranged, the closed form summation may have a
singularity at 0 because of a denominator term that works out as
sin(Pi/2 + Pi*A) where A is the lower bound on the summation; with A
being 0, that's going to give you a 0 in the denominator.

Other paths to finding the integral look like they might be fine (or at
least not involving a division by 0).

I think the division by 0 that Maple comes up with in some cases is
probably a bug in Maple; when I wake up more, I will write it up as a
bug report for them.

Again, I have no information as to how MuPad would attempt the same
calculation.



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