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MathGroup Archive 2006

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Re: sum of integrals over patial intervals != integral

  • To: mathgroup at smc.vnet.net
  • Subject: [mg71733] Re: [mg71719] sum of integrals over patial intervals != integral
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Tue, 28 Nov 2006 06:03:36 -0500 (EST)
  • Reply-to: hanlonr at cox.net

Works in my version:

$Version

5.2 for Mac OS X (June 20, 2005)

f[x_]:=Log[Sin[x]^2]Tan[x];

Integrate[f[x],{x,0,Pi}]

0


Bob Hanlon

---- Peter Pein <petsie at dordos.net> wrote: 
> Dear group,
> 
> I wanted Mathematica to show, that for f[x_]:=Log[Sin[x]^2]Tan[x], 
> Integrate[f[x],{x,0,Pi}]==0, because f[x]+f[Pi-x]==0.
> 
> Mathematica says Integrate[f[x],{x,0,Pi}] does not converge, but 
> Integrate[f[x],{x,0,Pi/2}] and Integrate[f[x],{x,Pi/2,Pi}] evaluate to 
> -Pi^2/12 resp. P^2/12 and the sum is zero. The more general integral 
> Integrate[f[x],{x,0,z},Assumptions->Pi/2<z<=Pi] evaluates explicitly (?).
> 
> What did I do wrong?
> http://people.freenet.de/Peter_Berlin/Mathe/komisch.nb
> 
> TIA,
> Peter
> 


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