       Re: simplifying definite vs indefinite integrals

• To: mathgroup at smc.vnet.net
• Subject: [mg90659] Re: simplifying definite vs indefinite integrals
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Fri, 18 Jul 2008 04:01:32 -0400 (EDT)
• Organization: Uni Leipzig
• References: <g5n464\$sbm\$1@smc.vnet.net>

```Hi,

Integrate[a[x] b[y], {y, s, t}] /.
Integrate[a_*b_, {x_, x0_, x1_}] /; FreeQ[a, x] :>
a*Integrate[b, {x, x0, x1}]

??

Regards
Jens

rikblok at gmail.com wrote:
> Hi Mathematica gurus (& sorry if this is a dupe post),
>
> I'm new to Mathematica and I was surprised to see that it handles
> definite versus indefinite integrals differently. For example:
>
> In:= indef = Integrate[a[x] b[y], y]
>
> Out= a[x] \[Integral]b[y] \[DifferentialD]y
>
> Nice.  a[x] gets pulled out of the integral.
>
> In:= def = Integrate[a[x] b[y], {y, s, t}]
>
> Out= \!\(
> \*SubsuperscriptBox[\(\[Integral]\), \(s\), \(t\)]\(\(a[x]\ b[
>     y]\) \[DifferentialD]y\)\)
>
> But not for the definite integral.  Why?  And how can I make it factor
> out?
>
> In:= Collect[def, a[x]]
>
> Out= \!\(
> \*SubsuperscriptBox[\(\[Integral]\), \(s\), \(t\)]\(\(a[x]\ b[
>     y]\) \[DifferentialD]y\)\)
>
> doesn't work. Nor does
>
> In:= Simplify[def]
>
> Out= \!\(
> \*SubsuperscriptBox[\(\[Integral]\), \(s\), \(t\)]\(\(a[x]\ b[
>     y]\) \[DifferentialD]y\)\)
>
> I can't even remove a[x] manually:
>
> In:= FullSimplify[def/a[x]]
>
> Out= \!\(
> \*SubsuperscriptBox[\(\[Integral]\), \(s\), \(t\)]\(\(a[x]\ b[
>     y]\) \[DifferentialD]y\)\)/a[x]
>
> Suggestions?  Thanks for your help!
>
> Rik
>

```

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