Use Green's Theorem to evaluate $\int_C \vec{F} \cdot d\vec{r}$, where
$\vec{F} = (\sqrt{x} + 6y, 2x + \sqrt{y})$
C consists of the arc of the curve $y = 3x - x^2$ from $(0,0)$ to $(3,0)$ and the line segment from $(3,0)$ to $(0,0)$.
Hint: Check the orientation of the curve before applying the theorem.