Re: Integrating over area of intersection

*To*: mathgroup at smc.vnet.net*Subject*: [mg44191] Re: Integrating over area of intersection*From*: koopman at sfu.ca (Ray Koopman)*Date*: Sat, 25 Oct 2003 06:27:02 -0400 (EDT)*References*: <bn8esp$nle$1@smc.vnet.net> <bnap4l$4jv$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

"Toni Danza" <nospam at yoohoo.com> wrote in message news:<bnap4l$4jv$1 at smc.vnet.net>... > Adding: > It would be really useful NOT to use the > Nintegrate[If[x^2 + y^2 < fJ^2 && ...,1,0],{x,-inf,inf},{y,-inf,inf}] > form, because it takes just waaaayyyy too long > > Ideally, I would like to extract the y boundary for every x to use as > integral limits , that should speed it up... If you're willing to do it numerically then this should get it: With[{xmin = Max[-fJ,f1-fH,f2-fH], xmax = Min[fJ,f1+fH,f2+fH]}, If[xmin >= xmax, 0, NIntegrate[<whatever>, {x,xmin,xmax}, {y,-Sqrt[Min[fJ^2-x^2, fH^2-(x-f1)^2, fH^2-(x-f2)^2]], Sqrt[Min[fJ^2-x^2, fH^2-(x-f1)^2, fH^2-(x-f2)^2]]}]]]