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)

```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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