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Evaluate the circulation of $\vec{F} = \langle -y, x \rangle$ about the boundary of a disk of radius 2 centered about the origin.

By Green's Theorem, $\oint_{\partial R} \vec{F} \cdot ds = 2\pi$

By Green's Theorem, $\oint_{\partial R} \vec{F} \cdot ds = 8\pi$

By Green's Theorem, $\oint_{\partial R} \vec{F} \cdot ds = -8\pi$

Since $\vec{F}$ is conservative and $\partial R$ is a closed curve, $\oint_{\partial R} \vec{F} \cdot ds = 0$

None of the Above