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: In steps, instead of in-lining: 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

**References**:**Applying the Integration Function to a List Of Regions***From:*"John Snyder" <jsnyder@wi.rr.com>