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Multivariable Calculus

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Moderate

Flux Calculation in First Octant Unit Sphere

MVCALC-1VECOY

Let $S$ be the boundary of the portion of the unit sphere that lies in the first octant. Calculate the flux of $\vec{F} = \left\langle x^3, y^3, z^3 \right\rangle$ outward through $S$.

A

$\cfrac{3\pi}{10}$

B

$\cfrac{3\pi}{5}$

C

$\cfrac{\pi}{10}$

D

$\cfrac{\pi}{15}$

E

None of the Above