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variable dimension of domain of integration


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


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