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## Homework Statement

Find the centre of mass of a uniform hemispherical shell of inner radius a and outer radius b.

## Homework Equations

##r_{CoM} = \sum \frac{m\vec{r}}{m}##

## The Attempt at a Solution

Using ##x(r,\theta,\phi)## for coordinates,

$$x_{CoM}=\frac{\int_{0}^{\frac{\pi}{2}}\int_{0}^{2\pi}\int_{a}^{b} \vec{x}\rho r^2\sin{\theta}drd\theta d\phi}{\int_{0}^{\frac{\pi}{2}}\int_{0}^{2\pi}\int_{a}^{b} \rho r^2\sin{\theta}drd\theta d\phi}$$

My vector calculus is rusty, how do I handle the ##\vec{x}## in this integral?