Calculus 3: Surface area

Compute the surface area of a surface given its parametric description. Use the formula: $\ iint_{\text{Region}} \| \mathbf{r}_u \times \mathbf{r}_v \| \, du \, dv$ where $\mathbf{r}_u$ and $\mathbf{r}_v$ are the partial derivatives of the position vector with respect to the parameters $u$ and $v$.