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Re: Multiple Integrals

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  • Subject: [mg117617] Re: Multiple Integrals
  • From: Bill Rowe <readnews at>
  • Date: Thu, 24 Mar 2011 06:31:34 -0500 (EST)

On 3/23/11 at 2:56 AM, jeanmichel.benkert at (schomi) wrote:

>I'm having troubles with multiple integrals in Mathematica and hope
>that you guys might be able to help me.

>Calculating a multiple integral per se is not such a big deal, for
>instance for n=2 the code would be of the form

>Integrate[f(x, y), {x, x_min, x_max}, {y, y_min,y_max}].

>What I'd like to have is a general formula for computing an
>intergral in R^n, ie of the form

>Integrate[f(x1, x2, ...., xn), {x1, x1_min, x1_max}, {x2,
>x2_min,x2_max}, ...., {xn, xn_min, xn_max}]

>The dots .... should of course be replaced by code. Is there a way
>to build something of this form?

Yes. Here is an example for a double integral.

In[18]:= expr = x y;
limits = {{1, 2}, {3, 4}};
vars = {x, y};

Obviously, the lists above could be extended to arbitrary length
and created via code. Here is the integral using the above:

In[21]:= Integrate[expr,
  Sequence @@ MapThread[Flatten@{##} &, {vars, limits}]]

Out[21]= 21/4

And to demonstrate the same result is obtained by conventional entry

In[22]:= Integrate[x y, {x, 1, 2}, {y, 3, 4}]

Out[22]= 21/4

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