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