Chapter 6.7, Problem 372E

For the following exercises, let $S$ he the disk enclosed by curve $C:\text{r}(t)=\langle \cos \phi \cos t,\sin t\sin \phi \cos t\rangle$ , for $0\le t\le 2\pi$ , where $0\le \phi \le \frac{\pi }{2}$ is a fixed angle.

372. Velocity field $\text{v =}\langle 0,1-x^2,0\rangle$ , for $\left|x\right|\le 1$ and $\left|z\right|\le 1$ , represents a horizontal flow in the $y$ -direction. Compute the curl of $\text{v}$ in a Clockwise rotation.