       Re: Applying the Integration Function to a List Of Regions

• To: mathgroup at smc.vnet.net
• Subject: [mg88782] Re: [mg88739] Applying the Integration Function to a List Of Regions
• From: "W_Craig Carter" <ccarter at mit.edu>
• Date: Fri, 16 May 2008 05:33:38 -0400 (EDT)
• References: <200805151051.GAA21829@smc.vnet.net>

```Hello John,

Here is a way to do this, but I am going to guess that you will get
more elegant responses:

temp = Map[Apply[f, #] &, regions];
temp /. f[a__] :> Integrate[1, a]       (*this takes a while on my machine*)

(*
returns
{(13 a^4)/8, -(1/3)
a ((a^2)^(3/2) (4 - 3 \[Pi]) + a^3 (13 + 3 \[Pi])), (13 a^4)/8, (
13 a^4)/8, 1/3 a^3 (-4 Sqrt[a^2] + a (-13 + 6 \[Pi])), (13 a^4)/8}
*)

Craig
On Thu, May 15, 2008 at 6:51 AM, John Snyder <jsnyder at wi.rr.com> wrote:
> 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
:
:
2 a}}};
>
> 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
:
:
>
> 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:
>

> There must be a way?
>
> Thanks,
>
> John
>
>
>

--
W. Craig Carter

```

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