MathGroup Archive 2006

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: sum of integrals over patial intervals != integral


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
> 


  • Prev by Date: RE: Descending order
  • Next by Date: Re: using a different stylesheet
  • Previous by thread: Re: Strange empty set of solutions
  • Next by thread: Re: sum of integrals over patial intervals != integral