Re: sum of integrals over patial intervals != integral

• To: mathgroup at smc.vnet.net
• Subject: [mg71779] Re: sum of integrals over patial intervals != integral
• From: "dimitris" <dimmechan at yahoo.com>
• Date: Wed, 29 Nov 2006 02:56:09 -0500 (EST)
• References: <ekh5hc\$rn5\$1@smc.vnet.net>

```Also

In[1]:=
\$Version
Out[1]=
"4.0 for Microsoft Windows (April 21, 1999)"

In[5]:=
f[x_] := Log[Sin[x]^2]*Tan[x];

In[20]:=
Off[\$MaxExtraPrecision::meprec]

In[21]:=
Integrate[f[x], {x, 0, Pi}]
N[%, 40]
Out[21]=
Pi^2/3 + 1/2*(-3*Log[2]^2 - Log[4]^2 + Log[2 - Sqrt[2]]^2 +
Log[16]*Log[2 + Sqrt[2]] - Log[2 + Sqrt[2]]^2 -
4*PolyLog[2, -(1/Sqrt[2])] - 4*PolyLog[2, 1/Sqrt[2]] + 4*PolyLog[2,
1 - 1/Sqrt[2]] - 2*PolyLog[2, 1/4*(2 - Sqrt[2])] -
4*PolyLog[2, 2/(2 + Sqrt[2])] - 2*PolyLog[2, 1/4*(2 + Sqrt[2])])
Out[22]=
-9.8933845188332`0.3443*^-92

Regards
Dimitris

Ï/Ç Bob Hanlon Ýãñáøå:
> 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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