# Gauss Bonnet theorem for hyperbolic triangle

the half circle is the graph of $\sqrt{1-x^2}$. To compute
$\int_{\Delta}{\frac{1}{y^2}dxdy}$, note the area $\Delta$ is bounded by x=a, x=b and the half circle. So we can compute the integral using iterated integrals by Fubini's theorem, for x from a to b, y from $\sqrt{1-x^2}$ to infinite.