Re: variable dimension of domain of integration

*To*: mathgroup at smc.vnet.net*Subject*: [mg115988] Re: variable dimension of domain of integration*From*: Ray Koopman <koopman at sfu.ca>*Date*: Fri, 28 Jan 2011 06:15:06 -0500 (EST)*References*: <ihrb36$8qe$1@smc.vnet.net>

On Jan 27, 12:41 am, Ulvi Yurtsever <a... at b.c> 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 F[n_] := NIntegrate[Sqrt@Sum[x[i]^2,{i,n}], Evaluate[ Sequence@@Table[{x[i],0,1},{i,n}]]]