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## Homework Statement

Please evaluate the integral [itex]\oint[/itex] d[itex]\vec{A}[/itex][itex]\cdot[/itex][itex]\vec{v}[/itex], where [itex]\vec{v}[/itex] = 3[itex]\vec{r}[/itex] and S is a hemisphere defined by |[itex]\vec{r}[/itex]| [itex]\leq[/itex]

*a*and

*z*≥ 0,

a) directly by surface integration.

b) using the divergence theorem.

## Homework Equations

-Divergence theorem in spherical coordinates

## The Attempt at a Solution

Another one where the [itex]\vec{r}[/itex] messes me up. Simple enough if it was in regular xyz. Plus the [itex]\vec{v}[/itex]... and I don't really know where to start.