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Re: variable dimension of domain of integration

  • To: mathgroup at smc.vnet.net
  • Subject: [mg115990] Re: variable dimension of domain of integration
  • From: Peter Pein <petsie at dordos.net>
  • Date: Fri, 28 Jan 2011 06:15:29 -0500 (EST)
  • References: <ihrb36$8qe$1@smc.vnet.net>

On 27.01.2011 09:41, Ulvi Yurtsever wrote:
> Consider the function $f(n) = \int_{{0,1}^n}
> \sqrt{\sum_{i=1}^{n} {x_i}^2} dx_1 ... dx_n$.
> How would you define a mathematica function
> F[n_] (using NIntegrate) that computes this
> integral over the n-cube? I can think of several
> inelegant solutions; but surely there are neat
> ways of doing things of this sort...
>
>
> thanks
>

ndim[n_] := NIntegrate @@
     Prepend[#, Sqrt@Tr[#[[All, 1]]^2]]&[Table[{x[i], 0, 1}, {i, n}]]



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