$1.$Use Green's Theorem to compute the counterclockwise circulation of F around the closed curve C$,$ where $C$ is the lobe of the lemniscate $r^2=sin2$ that lies in the first quadrant.

$F=(x-e^{x}cosy)i+(x+e^{x}siny)j$

A$.\frac{1}{2}$

B$.-\frac{1}{2}$

C$.0$

D$.\frac{1}{4}$