Use Green's Theorem to evaluate $\displaystyle \int_{{C}}\vec{{{F}}}\cdot{d}\vec{{{r}}}$, where

$\displaystyle \vec{{{F}}}={\left\langle\sqrt{{{x}}}+{3}{y},{2}{x}+\sqrt{{{y}}}\right\rangle}$

$\displaystyle {C}$ consists of the arc of the curve $\displaystyle {y}={2}{x}-{x}^{{2}}$ from (0,0) to (2,0) and the line segment from (2,0) to (0,0).

Preview Question 6  

Hint: Check the orientation of the curve before applying the theorem.