Re: variable dimension of domain of integration

*To*: mathgroup at smc.vnet.net*Subject*: [mg115981] Re: variable dimension of domain of integration*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Fri, 28 Jan 2011 06:13:47 -0500 (EST)

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 One possibility: f[n_] := Module[ {dims,x}, dims = Array[x,n]; NIntegrate[Evaluate[Sqrt[dims.dims]], Evaluate[Sequence@@Map[{#,0,1}&,dims]]] ] f[4] Out[20]= 1.1219 Daniel Lichtblau Wolfram Research