I want to compute $\int_{\mathbb{S}^n} f(y) d\mu (y)$ with $n=2$, $f$ defined on $\mathbb{S}^n$, and $\mu$ the Lebesgue measure on $\mathbb{S}^n$.
How do I evaluate this? Do I just replace $d\mu (y)$ with $\sin(\phi)d\phi d\theta$ after switching to spherical coordinates like with a normal surface integral?
Any help is appreciated! I've only worked with Lebesgue measure theoretically so far.