Re: How to integrate over a constrained domain
- To: mathgroup at smc.vnet.net
- Subject: [mg34218] Re: [mg34203] How to integrate over a constrained domain
- From: Andrzej Kozlowski <andrzej at platon.c.u-tokyo.ac.jp>
- Date: Fri, 10 May 2002 03:05:00 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
A little complicated looking, perhaps, but it can be done, (at least
when r is a real number).
In[1]:=
<<Experimental`
In[2]:=
Integrate[1, Sequence @@ ({#1[[3]], #1[[1]], #1[[5]]} & ) /@
List @@ GenericCylindricalAlgebraicDecomposition[
x^2 + y^2 <= 1, {x, y}][[1]]]
Out[2]=
Pi
Andrzej Kozlowski
Toyama International University
JAPAN
http://platon.c.u-tokyo.ac.jp/andrzej/
On Thursday, May 9, 2002, at 06:16 PM, Maciej Sobczak wrote:
> Hi,
>
> Let's say I have a set on a (x,y) plane given by:
>
> x^2 + y^2 < r^2
>
> and I want to compute its area.
> Yes, I know its Pi*r^2, but I want Mathematica tell me.
>
> As a generalization, I want to integrate over a domain given by one or
> more
> inequalities.
> The problem above can be solved like this:
>
> Integrate[1, {x, -r, r}, {y, -Sqrt[r^2-x^2], Sqrt[r^2-x^2]}]
> Simplify[%, {r>0}]
>
> which gives
>
> Pi r^2
>
> That's nice, but requires solving the inequality for y, which is not
> always
> viable.
>
> It would be nice to have syntax like:
>
> Integrate[1, {x, y}, {x^2 + y^2 < r^2}]
>
> but it does not work (of course).
>
> How can I achieve what I want?
>
> Cheers,
>
> --
> Maciej Sobczak
> http://www.maciejsobczak.com/
>
>
>
>
>
>