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