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Re: Why is this integral hard for mathematica?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg92853] Re: Why is this integral hard for mathematica?
*From*: dh <dh at metrohm.ch>
*Date*: Wed, 15 Oct 2008 05:37:31 -0400 (EDT)
*References*: <gcn466$710$1@smc.vnet.net>
Hi Kristian,
the anti-derivative has branch cuts. In this case you must figure what
branch you have to take. I guess that this is what Mathematica does.
E.g. set h=0.5;k=1;alpha=1 and integrate from 0 to 1
evaluate the integral and you get: 2.216..
now calculate the anti-derivative at 1 and 0 and take the difference,
you get: -1.537.. , this is wrong
Daniel
Kristian Schmidt wrote:
> Hello
>
> Consider this indefinite integral: Integrate[Sqrt[
> 4 k (1 + \[Alpha] (-1 + \[Epsilon])) + (h + \[Epsilon] -
> h \[Epsilon])^2], \[Epsilon]]
>
> This evaluates fine. Now try the same integral with limits of 1/2 and 3/2:
> Integrate[Sqrt[
> 4 k (1 + \[Alpha] (-1 + \[Epsilon])) + (h + \[Epsilon] -
> h \[Epsilon])^2], {\[Epsilon], 1/2, 3/2}]
>
> This hangs, and I haven't been patient enough to wait it out yet :)
>
> k and alpha are just real numbers, and 0<= h <= 1. Adding these assumptions didn't seem to help though.
>
> I cannot see why it hangs. If mathematica is able to compute the antiderivative just fine, isn't it just a matter of substracting the antiderivative with itself in the two limits?
>
--
Daniel Huber
Metrohm Ltd.
Oberdorfstr. 68
CH-9100 Herisau
Tel. +41 71 353 8585, Fax +41 71 353 8907
E-Mail:<mailto:dh at metrohm.com>
Internet:<http://www.metrohm.com>
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