       Re: variable dimension of domain of integration

• To: mathgroup at smc.vnet.net
• Subject: [mg115975] Re: variable dimension of domain of integration
• From: Leonid Shifrin <lshifr at gmail.com>
• Date: Fri, 28 Jan 2011 06:12:38 -0500 (EST)

Hi Ulvi,

I would do this:

In:= Clear[f];
f[n_] :=
With[{vars = Table[Unique[], {n}]},
NIntegrate @@ {Total[vars^2],
Sequence @@ Table[{v, 0, 1}, {v, vars}]}]

In:= f /@ Range

Out= {0.333333, 0.666667, 1., 1.33333, 1.66667}

This basically constructs programmatically the same NIntegrate that you
would write by hand,
so not sure if this can be called elegant.

Regards,
Leonid

On Thu, Jan 27, 2011 at 11:41 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
>
>



• Prev by Date: Re: About Table
• Next by Date: Anyone know of a book on Mathematica suitable for 16-18 year old?
• Previous by thread: Re: variable dimension of domain of integration
• Next by thread: Select non-mathematica font for graphics ?