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



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