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