       Re: Double integral of a piecewise-constant function

• To: mathgroup at smc.vnet.net
• Subject: [mg61515] Re: Double integral of a piecewise-constant function
• From: Chris Rodgers <rodgers at physchem.NOSPAMox.aREMOVEc.uk>
• Date: Fri, 21 Oct 2005 00:38:00 -0400 (EDT)
• Organization: Oxford University, England
• References: <200510180644.CAA11181@smc.vnet.net> <dj4q2v\$ipv\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```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 = 0 to 3 and t = 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, 0, t}], {t, 0, 3}]

2) Integrate[testfunc, {t, 0, 3}, {t, 0, t}]

3) Integrate[
Integrate[testfunc, {t, 0, t},
Assumptions -> t \[Element] Reals], {t, 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 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 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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