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Re: Expanding Integrals with constants and 'unknown'

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  • Subject: [mg110070] Re: Expanding Integrals with constants and 'unknown'
  • From: Mark McClure <mcmcclur at>
  • Date: Tue, 1 Jun 2010 04:21:08 -0400 (EDT)

On Sun, May 30, 2010 at 11:45 PM, Jesse Perla <jesseperla at> wrote:
> I have an integral involving constants and an 'unknown' function.  I
> would like to expand it out to solve for the constants and keep the
> integrals of the unknown function as expected.
> i.e.
> Integrate[a + z + s[z], {z, clow, chigh}]
> I want to get out:
> (a*chigh + chigh^2/2 - a*clow - clow^2/2) + Integrate[s[z], {z, clow,
> chigh}]

You could write a function that is explicitly linear but calls
Integrate otherwise.  Here's a small modification of your example that
also illustrates constant multiples.

In[70]:== Clear[int];
int[expr_Plus, {var_, low_, high_}] :==
  Map[int[#, {var, low, high}] &, expr];
int[expr_Times, {var_, low_, high_}] :== With[
   {c == Select[expr, FreeQ[#, var] &]},
   c*int[expr/c, {var, low, high}]];
int[expr_, {var_, low_, high_}] :== Integrate[expr,
   {var, low, high}];
int[a + z + 5 c*s[z], {z, clow, chigh}] // InputForm

chigh^2/2 + a*(chigh - clow) - clow^2/2 +
 5*c*Integrate[s[z], {z, clow, chigh}]

Mark McClure

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