What the work of the field vector $\displaystyle F(x,y) = (x^2,xy)$ to move a particle along the trajectory $\displaystyle r(t) = (2cost,2sint)$ for $\displaystyle 0 \leq t \leq 2 \pi$

My solution:

$\displaystyle \int_0^{2 \pi} (-8cos^2tsent + 8cos^2tsent)dt$

$\displaystyle = 0$

Is correct ?