Re: sum of integrals over patial intervals != integral

• To: mathgroup at smc.vnet.net
• Subject: [mg71778] Re: sum of integrals over patial intervals != integral
• From: "dimitris" <dimmechan at yahoo.com>
• Date: Wed, 29 Nov 2006 02:56:08 -0500 (EST)
• References: <ekh5hc\$rn5\$1@smc.vnet.net>

```In[4]:=
\$Version
Out[4]=
"5.2 for Microsoft Windows (June 20, 2005)"

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

In[3]:=
Integrate[f[x], {x, 0, Pi}]
Integrate::"idiv" : "Integral of \
\!\(\(\(Log[\(\(\(Sin[x]\)\^2\)\)]\)\)\\ \(\(Tan[x]\)\)\) does not
converge \
on \!\({x, 0, \
\
ButtonFrame->None, ButtonData:>\"Integrate::idiv\"]\)"
Out[3]=
Integrate[Log[Sin[x]^2]*Tan[x], {x, 0, Pi}]

But

In[5]:=
Integrate[f[x], {x, 0, Pi/2, Pi}]
Out[5]=
0

In[9]:=
Integrate[Log[Sin[x]^2]*Tan[x], {x, 0, Pi},
GenerateConditions -> False]
Out[9]=
0

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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