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 >