Re: Multiple Integrals
- To: mathgroup at smc.vnet.net
- Subject: [mg117589] Re: Multiple Integrals
- From: Ray Koopman <koopman at sfu.ca>
- Date: Thu, 24 Mar 2011 06:26:22 -0500 (EST)
- References: <imc95n$1kl$1@smc.vnet.net>
On Mar 23, 12:57 am, schomi <jeanmichel.benk... at gmail.com> wrote:
> Hi everybody
>
> 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?
>
> Any help would be appreciated. In case I am not making myself clear,
> do not hesitate to ask question and I'll try to give you a better
> explanation.
>
> Thanks a lot!
>
> schomi
mint[f_,lims_] := Block[{X,x}, X = Array[x,Length@lims];
Integrate[f@X,Sequence@@MapThread[Prepend,{lims,X}]]]
func = Times@@(#^Range@Length@#)& ;
ab = {{a1,b1},{a2,b2},{a3,b3}};
mint[func,ab] == Integrate[x1 x2^2 x3^3,
{x1,a1,b1},{x2,a2,b2},{x3,a3,b3}]
True
Note that the argument that is passed to f is a *list*
{x[1],...,x[n]}, not a *sequence* x[1],...,x[n].