# Evaluating integral on surfaces

1. Mar 25, 2012

### Goklayeh

Hello everyone! Could someone tell me how to evaluate the integral
$$\int_{B_{\delta}(p_0)}{\frac{1}{(1 + d^2(p_0, p))^2}\mathrm{d}v_g(p)}$$
where $B_{\delta}(p_0) \subset M$ and $(M, g)$ is a generic compact surface and $\delta > 0$ can be made small as one wishes (as usual, $d$ is the intrinsic metric)? Thanks you in advance

P.S. I strongly suspect that the value should be $\pi$, but I'm a newbie in integration-on-manifold without any idea about how to proceed.