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>
- Reply-to: kuska at informatik.uni-leipzig.de
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[1]:= indef = Integrate[a[x] b[y], y]
>
> Out[1]= a[x] \[Integral]b[y] \[DifferentialD]y
>
> Nice. a[x] gets pulled out of the integral.
>
> In[2]:= def = Integrate[a[x] b[y], {y, s, t}]
>
> Out[2]= \!\(
> \*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[3]:= Collect[def, a[x]]
>
> Out[3]= \!\(
> \*SubsuperscriptBox[\(\[Integral]\), \(s\), \(t\)]\(\(a[x]\ b[
> y]\) \[DifferentialD]y\)\)
>
> doesn't work. Nor does
>
> In[4]:= Simplify[def]
>
> Out[4]= \!\(
> \*SubsuperscriptBox[\(\[Integral]\), \(s\), \(t\)]\(\(a[x]\ b[
> y]\) \[DifferentialD]y\)\)
>
> I can't even remove a[x] manually:
>
> In[5]:= FullSimplify[def/a[x]]
>
> Out[5]= \!\(
> \*SubsuperscriptBox[\(\[Integral]\), \(s\), \(t\)]\(\(a[x]\ b[
> y]\) \[DifferentialD]y\)\)/a[x]
>
> Suggestions? Thanks for your help!
>
> Rik
>