Re: Applying the Integration Function to a List Of

• To: mathgroup at smc.vnet.net
• Subject: [mg88759] Re: [mg88739] Applying the Integration Function to a List Of
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Fri, 16 May 2008 05:29:13 -0400 (EDT)

```Simplified version

regions = {{{x, 0, a}, {cx, 0, b}, {y, 0, c}, {cy, 0, d}}, {{x, 0, 2 a}, {cx,
0, b}, {y, 0, c}, {cy, 0, d}}, {{x, 0, a}, {cx, 0, 3 b}, {y, 0, c}, {cy,
0, d}}};

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

{a b c d,2 a b c d,3 a b c d}

Bob Hanlon

---- 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
> 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
> a-Sqrt[a^2-cx^2+2 cx x-x^2]},{cy,-Sqrt[a^2-cx^2+2 cx
> x-x^2]+y,Sqrt[a^2-cx^2+2 cx x-x^2]+y}},{{x,0,a},{cx,0,a+x},{y,2
> a-Sqrt[a^2-cx^2+2 cx x-x^2],2 a},{cy,-Sqrt[a^2-cx^2+2 cx x-x^2]+y,2
> a}},{{x,a,2 a},{cx,-a+x,2 a},{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,a,2 a},{cx,-a+x,2
> a},{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 x-x^2]+y,Sqrt[a^2-cx^2+2 cx
> x-x^2]+y}},{{x,a,2 a},{cx,-a+x,2 a},{y,2 a-Sqrt[a^2-cx^2+2 cx x-x^2],2
> a},{cy,-Sqrt[a^2-cx^2+2 cx x-x^2]+y,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
> 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
> x-x^2]+y,Sqrt[a^2-cx^2+2 cx x-x^2]+y}],Integrate[1,{x,0,a},{cx,0,a+x},{y,2
> a-Sqrt[a^2-cx^2+2 cx x-x^2],2 a},{cy,-Sqrt[a^2-cx^2+2 cx x-x^2]+y,2
> a}],Integrate[1,{x,a,2 a},{cx,-a+x,2 a},{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,a,2 a},{cx,-a+x,2
> a},{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 x-x^2]+y,Sqrt[a^2-cx^2+2 cx
> x-x^2]+y}],Integrate[1,{x,a,2 a},{cx,-a+x,2 a},{y,2 a-Sqrt[a^2-cx^2+2 cx
> x-x^2],2 a},{cy,-Sqrt[a^2-cx^2+2 cx x-x^2]+y,2 a}]}
>
> 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
>
> But I can't figure out how to incorporate the 1 as the integrand when I try
> to set this up automatically.
>
> There must be a way?
>
> Thanks,
>
> John
>
>

```

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