       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>...
> 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]]}]]]

```

• Prev by Date: Re: Antw: pdf-export
• Next by Date: Re: ProductLog[-Pi/2]
• Previous by thread: Re: Integrating over area of intersection
• Next by thread: Re: Integrating over area of intersection