RE: RE: Re: How to integrate over a constrained domain
- To: mathgroup at smc.vnet.net
- Subject: [mg34258] RE: [mg34246] RE: [mg34217] Re: [mg34203] How to integrate over a constrained domain
- From: "DrBob" <majort at cox-internet.com>
- Date: Sun, 12 May 2002 03:26:03 -0400 (EDT)
- Reply-to: <drbob at bigfoot.com>
- Sender: owner-wri-mathgroup at wolfram.com
>>It's NOT undocumented -- in the Help Browser, go to Add-ons, Standard Packages, Calculus, Integration. OK, but there's no particular reason for a function that turns True/False into 1/0 to be (a) part of an add-on, (b) related to Calculus, or (c) involved specifically in Integration. Why would I look for it there? That's what I call "undocumented"... you can find it only if you've ALREADY found it... and didn't forget where. It should be mentioned in the documentation of True, False, TrueQ, If, etc. It's also conceptually related to UnitStep, DiracDelta, etc. And yes, definitely, it should be in the Master Index! Bobby -----Original Message----- From: Murray Eisenberg [mailto:murraye at attbi.com] To: mathgroup at smc.vnet.net Subject: [mg34258] Re: [mg34246] RE: [mg34217] Re: [mg34203] How to integrate over a constrained domain 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: [mg34258] [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