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Re: Integrating over area of intersection


"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]]}]]]


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