Use Green's Theorem to evaluate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r),$ where

vec$(F)=($:$\sqrt[\phantom{2}]{x}+5y,2x+\sqrt[\phantom{2}]{y}$:$)$

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

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