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>