$(1$ point$)$

Verify if the vector field $F=($:$xcos(2y),-x^{2}sin(2y)$:$)$ is conservative and evaluate the line integral

${\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*dR$

where $C$ is the curve parameterized by $R=$ for $0t1.$

A$.I=-\frac{sin(4)}{4}$

B$.I=0$

C$.I=\frac{cos(4)}{2}$

D$.I=-\frac{2}{2}$

E$.I=-\frac{cos(2)}{2}$