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Multivariable Calculus

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Flux Through Glove: $\vec{F} = \langle 3xy^2, -y^3, 9 \rangle$

MVCALC-VEKAGV

Let the unit circle $C$ be the boundary of the surface $S$. The unit circle​ $C$ lies on the $x$-$y$ plane. Calculate the flux of:

$$\vec{F} = \langle 3xy^2, -y^3, 9 \rangle$$

...upwards across $S$. See the figure below:

A

$\pi\sqrt{3}$

B

$3\pi$

C

$9\pi$

D

$(3-\sqrt{3})\pi$

E

None of the Above