Figure 3 on the next page shows the region that you're integrating over and where and are coming from. For , you're integrating from the top of the unit circle to infinity.
I wasnt sure where to post this but im having trouble understanding a part of this proof, the integration part, could anyone explain to me where the intervals infinite and sqrt(1-x^2), and beta, pi - alpha come from in the integrals on the proof on page 3 of: http://www.maths.manchester.ac.uk/~c.../lecture07.pdf
i remember how to integrate double integrals and everything, its just i don't understand why there is sqrt(1-x^2) ive looked in my old textbook for calculus and it doesnt have anything there
hmmm i'm not sure if im getting it right, is it because like the equation of a circle x^2 + y^2 = r but r = 1 so to get y we have sqrt(1-x^2), i know this isnt exactly right but am i on the right lines