       Re: Integrate with unknow function

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• Subject: [mg130230] Re: Integrate with unknow function
• From: "shan@mitbbs" <shan.pub at gmail.com>
• Date: Sun, 24 Mar 2013 04:17:05 -0400 (EDT)
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Hi Murray,

I'm sorry for my inaccurate expression. Basically, f is a function without
definition until the Integrate function. Also, I should say the expecting
result is Integrate[f[d],2,3].

I tried the TagSetDelayed method offered by Jens in
http://mathematica.stackexchange.com/questions/5610/how-to-simplify-symbolic-integration

But it doesn't work with mathematica 9. Even it works, it requires some
fuction ff to be the indefinite integral of f, which is not my real case.

To be precise, I have two functions f1 and f2, i.e.,
f1=Integrate[f11[x],{x,0,a1}]+Integrate[f12[x],{x,a1,k}]
f2=Integrate[f21[x],{x,0,a2}]+Integrate[f22[x],{x,a2,k}]
where f11,f12,f21,f22 have no exact forms, and 0<a1<a2<k.

I tried to solve f1-f2, which should be [image:
[;\int_0^{a1}(f11[x]-f21[x])dx+\int_{a1}^{a2}(f12[x]-f21[x])dx+\int_{a2}^{k}(f12[x]-f22[d])dx;]]

I know it may be the case that some of the integral may not exist. But if
all of them are valid, how can I get the desired result? Thanks so much!

On Sat, Mar 23, 2013 at 7:13 AM, Murray Eisenberg <murray at math.umass.edu>wrote:

> Either I'm not understanding something here or you didn't explain the
> situation precisely. . .
>
> Is f just a symbol, or is there already an actual definition in the form
> f[d_] := (some expression in d) ?
>
> In any case, when you integrate with respect to d, that's a "dummy
> variable", so you would never expect to get an answer with a d in it.
>
> At the very best, you might hope that the difference reduces to
> Integrate[f[d], {d, 2, 3}], for a specific function f.
>
> Incidentally, d is probably a very bad name for the variable of
> integration!
>
> On Mar 23, 2013, at 3:25 AM, Shan <shan.pub at gmail.com> wrote:
>
> > Hi,
> >
> > I have a very rookie question as follows:
> >
> > Integrate[f[d], {d, 0,3}] - Integrate[f[d], {d, 0,2}]
> >
> > How can I get the result as f[d]? Thanks very much for any help!
> >
> > shan
>
> ---
> Murray Eisenberg                                    murray at math.umass.edu
> Mathematics & Statistics Dept.
> Lederle Graduate Research Tower            phone 413 549-1020 (H)
> University of Massachusetts                               413 545-2838 (W)
> 710 North Pleasant Street                         fax   413 545-1801
> Amherst, MA 01003-9305
>
>
>
>
>
>



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