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MathGroup Archive 2005

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Re: Integrate and Boole problems

  • To: mathgroup at smc.vnet.net
  • Subject: [mg58439] Re: Integrate and Boole problems
  • From: "Chris" <topher at csh.rit.edu>
  • Date: Sat, 2 Jul 2005 04:06:59 -0400 (EDT)
  • References: <da0bq0$fm8$1@smc.vnet.net><da2mk4$92e$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

I'm sorry, it must have pasted incorrectly, it wasn't an equal sign, it
was a less than or equal.

Integrate[Boole[((x - 1)^2 + y^2 + z^2 - 3^2)*((x + 1)^2 + y^2 + z^2 -
3^2) <= 0], {x, -Infinity, Infinity}, {y, -Infinity, Infinity}, {z, -
            Infinity, Infinity}]


Mathematica 5.1 is able to integrate over Boolean defined regions, so
in effect if you can define a region with inequalities, integrating
over it will return it's area (if two dimensional) or volume (as is the
case above). More about it can be found here:

http://www.wolfram.com/products/mathematica/newin51/integrationregions.html


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