Re: simplifying definite vs indefinite integrals
- To: mathgroup at smc.vnet.net
- Subject: [mg90689] Re: simplifying definite vs indefinite integrals
- From: Rik Blok <rikblok at gmail.com>
- Date: Sat, 19 Jul 2008 04:50:38 -0400 (EDT)
- References: <g5n464$sbm$1@smc.vnet.net> <g5piu6$qab$1@smc.vnet.net>
Thanks Jens! With a ReplaceRepeated it works great, even for more
complicated expressions!
In[131]:= ruleFactorDefInt =
Integrate[a_*b_, {x_, x0_, x1_}] /; FreeQ[a, x] :>
a*Integrate[b, {x, x0, x1}];
In[132]:= Integrate[
a[x]^2 b[y] c[x] / Sqrt[d[x] + 1] e[y], {y, s,
t}] //. ruleFactorDefInt
Out[132]= (a[x]^2 c[x] \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(s\), \(t\)]\(\(b[y]\ e[
y]\) \[DifferentialD]y\)\))/Sqrt[1 + d[x]]
Now I'm off to learn *why* it works...
Cheers,
Rik
On Jul 18, 1:06 am, Jens-Peer Kuska <ku... at informatik.uni-leipzig.de>
wrote:
> 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
>
> rikb... 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 fac=
tor
> > 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