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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


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