simplifying definite vs indefinite integrals

*To*: mathgroup at smc.vnet.net*Subject*: [mg90649] simplifying definite vs indefinite integrals*From*: rikblok at gmail.com*Date*: Thu, 17 Jul 2008 05:36:57 -0400 (EDT)

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