Re: Applying the Integration Function to a List Of Regions

• To: mathgroup at smc.vnet.net
• Subject: [mg88792] Re: Applying the Integration Function to a List Of Regions
• From: dh <dh at metrohm.ch>
• Date: Fri, 16 May 2008 05:35:33 -0400 (EDT)
• References: <g0h4me\$lbl\$1@smc.vnet.net>

```
Hi John,

you may try:

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

I used myIntegrate that you can see what is going on. If you replace

thsi by Integrate, Mathematica tries to evaluate the integrals.

hope this helps, Daniel

John Snyder 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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