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Use Green's theorem to evaluate $\int_C \mathbf{F} \cdot d\mathbf{r}$. (Check the orientation of the curve before applying the theorem.)
$\mathbf{F}(x, y) = \langle y - \cos(y), x \sin(y) \rangle$, C is the circle $(x - 6)^2 + (y + 2)^2 = 16$ oriented clockwise