Re: Applying the Integration Function to a List Of Regions

• To: mathgroup at smc.vnet.net
• Subject: [mg88772] Re: Applying the Integration Function to a List Of Regions
• From: Albert Retey <awnl at arcor.net>
• Date: Fri, 16 May 2008 05:31:42 -0400 (EDT)
• References: <g0h4me\$lbl\$1@smc.vnet.net>

```Hi,
> Assume that I have already determined a list of 4 dimensional regions as
> follows:
>
> regions={{{x,0,a},{cx,0,a+x},{y,0,Sqrt[a^2-cx^2+2 cx
> x-x^2]},{cy,0,Sqrt[a^2-cx^2+2 cx
> x-x^2]+y}},{{x,0,a},{cx,0,a+x},{y,Sqrt[a^2-cx^2+2 cx x-x^2],2
>
> I want to integrate over each of these regions using an integrand of 1. I
> want my output to be as follows:
>
> {Integrate[1,{x,0,a},{cx,0,a+x},{y,0,Sqrt[a^2-cx^2+2 cx
> x-x^2]},{cy,0,Sqrt[a^2-cx^2+2 cx
> x-x^2]+y}],Integrate[1,{x,0,a},{cx,0,a+x},{y,Sqrt[a^2-cx^2+2 cx x-x^2],2
> a-Sqrt[a^2-cx^2+2 cx x-x^2]},{cy,-Sqrt[a^2-cx^2+2 cx
>
> How can I do that without having to set up each of the integrals manually?
> I am looking for some way to do something like:
>
> Integrate @@ regions
>
> or
>
> Integrate @@@ regions

or:

Integrate[1, ##] & @@@ regions

If you wonder about the ## and & look up Function in the documentation
center.

hth,

albert

```

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