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Re: volume calculation

• To: mathgroup at smc.vnet.net
• Subject: [mg100262] Re: volume calculation
• From: Sebastian <meznaric at gmail.com>
• Date: Fri, 29 May 2009 21:00:20 -0400 (EDT)
• References: <gvn74b$ets$1@smc.vnet.net>

On May 29, 12:35 am, Filippo Miatto <mia... at gmail.com> wrote:
> Dear all,
> I need a way to find the volume of a multidimensional shape in the  
> coordinates (x1,x2,x3,...,xn), that comes from an inequality like  
> D(x1,x2,x3,...,xn) < L (with 3 variables i get a nice weird shape in  
> R^3, with more i don't plot it)
> In other words I let Mathematica calculate where in the space of the  
> solutions the inequality is solved and i'd like to have the numerical  
> "volume of the solutions".
> What strategy should i use? The function D is not invertible...
> Thank you,
> Filippo
>
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Try Monte Carlo integration, that's probably the easiest way to do
high dimensional integrals. Of course this will only work if you are
happy with a numerical result.