Suppose $\vec{F}(x,y) = \langle e^x, e^y \rangle$ and $C$ is the portion of the ellipse centered at the origin from the point $(0,1)$ to the point $(4,0)$ centered at the origin oriented clockwise.

(a) Find a vector parametric equation $\vec{r}(t)$ for the portion of the ellipse described above for $0 \leq t \leq \pi/2$.
$\vec{r}(t) =$

(b) Using your parametrization in part (a), set up an integral for calculating the circulation of $\vec{F}$ around $C$.
$\displaystyle \int_C \vec{F} \cdot d \vec{r} = \int_a^b \vec{F}(\vec{r}(t)) \cdot \vec{r}\,'(t) \, dt = \int_a^b$ $dt$
with limits of integration $a =$ and $b =$

(c) Find the circulation of $\vec{F}$ around $C$.
Circulation =