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 >