1. ## hyperbolic triangle proof

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

2. Figure 3 on the next page shows the region $\displaystyle \Delta$ that you're integrating over and where $\displaystyle a$ and $\displaystyle b$ are coming from. For $\displaystyle y$, you're integrating from the top of the unit circle to infinity.

3. so is sqrt(1-x^2) just the top of the unit circle?

4. This is the standard way to evaluate a double integral by iteration. Are you familair with double and triple integration over two and three dimensional regions?

5. Its been 2 years since ive done any integration whatsover, ive forgotton most of the double/triple integrals

6. 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

7. You should review double integration and in particular evaluating them through iteration. It'll all be clear after that.

8. ok thanks