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
>
>