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Multivariable Calculus

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Moderate

Circulation Disk Boundary Minus yx

MVCALC-TECNMK

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

A

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

B

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

C

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

D

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

E

None of the Above