Re: Integrating over area of intersection

*To*: mathgroup at smc.vnet.net*Subject*: [mg44187] Re: Integrating over area of intersection*From*: "Toni Danza" <nospam at yoohoo.com>*Date*: Sat, 25 Oct 2003 06:26:47 -0400 (EDT)*References*: <bn8esp$nle$1@smc.vnet.net> <bnaodq$4g8$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Yes, I have tried that, but it takes literally over an hour to finish... In the process it keeps complaining about lack of convergence. NIntegrate[If[...],...] is attempting to integrate a discontinuous function, causing mayhem in convergence algorithms.... OTOH, the integration limits are readily available, all I need to do is figure out how to plug the result of Reduce[region,{x,y}] into the limits of NIntegrate. The function will be nice and continuous here, should be no problem Any ideas? "Steve Luttrell" <luttrell at _removemefirst_westmal.demon.co.uk> wrote in message news:bnaodq$4g8$1 at smc.vnet.net... > Here is an example of the sort of thing you can do. > > First of all read in the Calculus`Integration` package which gives you the > Boole function for doing integrals over regions defined by inequalities: > > << Calculus`Integration` > > Now integrate the function x^2*y^2 (as an example) over the region of > interest (as an example fJ = 3, fH = 2, f1 = 1/2, f2 = -4^(-1)}): > > With[{fJ = 3, fH = 2, f1 = 1/2, f2 = -4^(-1)}, > Integrate[Boole[x^2 + y^2 < fJ^2 && > (x - f1)^2 + y^2 < fH^2 && (x - f2)^2 + y^2 < > fH^2]*x^2*y^2, {x, -Infinity, Infinity}, > {y, -Infinity, Infinity}]] > > which gives the result: > > -((56359*Sqrt[247])/163840) + (11/3)*ArcCos[3/16] + > (35/6)*ArcSin[Sqrt[13/2]/4] > > -- > Steve Luttrell > West Malvern, UK > > "Toni Danza" <nospam at yoohoo.com> wrote in message > news:bn8esp$nle$1 at smc.vnet.net... > > OK, I have three functions that are defined within their respective > circles. > > I would like to integrate over the intersection of the three circles. > > > > Here's what I have done: > > define region of integration: > > region = x^2 + y^2 < fJ^2 && (x - f1)^2 + y^2 < fH^2 && (x - f2)^2 + > y^2 > > < fH^2 > > > > Then I try to solve for the intersection using > > > > Reduce[region,{x,y}] > > > > and the result is something like (only works with numerical parameters...) > > > > -0.4<x<0.3 && sqrt(....)< y <sqrt(...) || -0.3<x<-0.2 && sqrt(....)< y > > <sqrt(...) > > > > How do I use this result to do integration over the region? > > > >