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Integrating over area of intersection


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?


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