MathGroup Archive 2002

[Date Index] [Thread Index] [Author Index]

Search the Archive

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




  • Prev by Date: RE: combining surface graphics objects
  • Next by Date: Re: combining surface graphics objects
  • Previous by thread: Re: Removed[] pop-visiting explanation?
  • Next by thread: Re: RE: RE: Re: How to integrate over a constrained domain