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MathGroup Archive 2005

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Re: Re: Double integral of a piecewise-constant function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg61546] Re: [mg61515] Re: Double integral of a piecewise-constant function
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Sat, 22 Oct 2005 00:35:33 -0400 (EDT)
  • Reply-to: hanlonr at cox.net
  • Sender: owner-wri-mathgroup at wolfram.com

You can state the assumption upfront.

Assuming[{Element[t[1], Reals]},
  Integrate[Integrate[testfunc, {t[2], 0, t[1]}], {t[1], 0, 3}]]


Bob Hanlon

> 
> From: Chris Rodgers <rodgers at physchem.NOSPAMox.aREMOVEc.uk>
To: mathgroup at smc.vnet.net
> Date: 2005/10/21 Fri AM 12:38:00 EDT
> Subject: [mg61546] [mg61515] Re: Double integral of a piecewise-constant function
> 
> OK. Here is a simpler example where I try to integrate a 
> piecewise-constant function in two dimensions.
> 
> I define a very simple function ("testfunc") with constant values in 1x1 
> squares over the domain t[1] = 0 to 3 and t[2] = 0 to 3 with value zero 
> elsewhere.
> 
> I then proceed to integrate a triangular region of this surface, whose 
> integral should be 1+2+3=6. I tried three different approaches:
> 
> 1) Integrate[Integrate[testfunc, {t[2], 0, t[1]}], {t[1], 0, 3}]
> 
> 2) Integrate[testfunc, {t[1], 0, 3}, {t[2], 0, t[1]}]
> 
> 3) Integrate[
>    Integrate[testfunc, {t[2], 0, t[1]},
>      Assumptions -> t[1] \[Element] Reals], {t[1], 0, 3}]
> 
> In (2) and (3), Mathematica succeeds, but in case (1) it doesn't.
> 
> Why does Mathematica not understand that the dummy variable t[1] is Real 
> in case (1)?
> 
> Although this example is trivial, in the work that I am trying to do, it 
> will be much more difficult to collect all the integrals together into a 
> single term. Is there any way to make the inner Integrate(s) realise 
> that t[1] is Real automatically? Can this be scaled up to the case where 
>   I have more than two Integrate's within one-another?
> 
> Yours,
> 
> Chris Rodgers.
> 
> P.S. A workbook containing these formulae and a plot of "testfunc" is 
> available at
> 
> http://physchem.ox.ac.uk/~rodgers/MMA/Problem1.nb
> 
> and a PDF showing the output is available at
> 
> http://physchem.ox.ac.uk/~rodgers/MMA/Problem1.pdf
> 
> 


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