# hyperbolic triangle proof

#### ojones

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.

• Purslow

#### Purslow

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

#### ojones

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?

#### Purslow

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

#### Purslow

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

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#### ojones

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

ok thanks