Re: RE: Re: How to integrate over a constrained domain
- To: mathgroup at smc.vnet.net
- Subject: [mg34256] Re: [mg34246] RE: [mg34217] Re: [mg34203] How to integrate over a constrained domain
- From: Murray Eisenberg <murraye at attbi.com>
- Date: Sun, 12 May 2002 03:25:59 -0400 (EDT)
- Organization: Mathematics & Statistics, Univ. of Mass./Amherst
- References: <200205110805.EAA21912@smc.vnet.net>
- Reply-to: murray at math.umass.edu
- Sender: owner-wri-mathgroup at wolfram.com
It's NOT undocumented -- in the Help Browser, go to Add-ons, Standard Packages, Calculus, Integration. However, it IS missing from the Master Index! DrBob wrote: > > Boole --- another undocumented feature. Sigh... > > Bobby > > -----Original Message----- > From: BobHanlon at aol.com [mailto:BobHanlon at aol.com] To: mathgroup at smc.vnet.net > Subject: [mg34256] [mg34246] [mg34217] Re: [mg34203] How to integrate over a constrained > domain > > In a message dated 5/9/02 6:42:13 AM, maciej at maciejsobczak.com writes: > > >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? > > For specific numeric values it is easy > > Needs["Calculus`Integration`"]; > > Table[{r, > > Integrate[Boole[ x^2+y^2<r^2] , > > {x,-r,r}, {y,-r,r}]}, > > {r,0,5}] > > {{0, 0}, {1, Pi}, {2, 4*Pi}, {3, 9*Pi}, {4, 16*Pi}, > > {5, 25*Pi}} > > Bob Hanlon > Chantilly, VA USA -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street Amherst, MA 01375
- References:
- RE: Re: How to integrate over a constrained domain
- From: "DrBob" <majort@cox-internet.com>
- RE: Re: How to integrate over a constrained domain