Re: Distribution and Integral
- To: mathgroup at smc.vnet.net
- Subject: [mg59882] Re: Distribution and Integral
- From: Peter Pein <petsie at dordos.net>
- Date: Wed, 24 Aug 2005 06:32:23 -0400 (EDT)
- References: <deeo66$2vq$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
ms_usenet at gmx.de schrieb:
> Hello,
>
> to apply further rules on simpler integrals (rules for the integration
> by parts), I would like to distribute the integral over its summands.
> This works if it is an integral alone, but doesn't if there is a factor
> (because the head is Integrate in the first, and Times in the latter
> case?):
>
> \!\(Distribute[
> t \(\[Integral]\_x1\%x2\((f[x] +
> g[x])\) \[DifferentialD]x\)]\[IndentingNewLine]
> Distribute[\[Integral]\_x1\%x2\((f[x] + g[x])\) \[DifferentialD]x]\)
>
> Out[695]=
> \!\(t\ \(\[Integral]\_x1\%x2\((f[x] + g[x])\) \[DifferentialD]x\)\)
> Out[696]=
> \!\(\[Integral]\_x1\%x2 f[x] \[DifferentialD]x + \[Integral]\_x1\%x2 g[
> x] \[DifferentialD]x\)
>
> How could I get the distribution in the latter case? Because f and g
> can have variable structure, I haven't found a simple rule with
> patterns. A hint to simplify the original problem, integration by
> parts, would be appreciated too!
>
> Best Regards,
> Martin
>
Hallo Martin,
I guess this _is_ a simple solution using patterns:
In[1]:=
t*Integrate[f[x] + g[x], {x, x1, x2}] /. i_Integrate :> Distribute[i]
Out[1]=
t*(Integrate[f[x], {x, x1, x2}] + Integrate[g[x], {x, x1, x2}])
--
Peter Pein, Berlin
GnuPG Key ID: 0xA34C5A82
http://people.freenet.de/Peter_Berlin/