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Multivariable Calculus

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Moderate

Average Value

MVCALC-1ENXRL

Find the average value of $f(x,y,z)=xz\sin^2(xy)$ on the domain $D=[0,\pi]\times [0,\pi] \times [0,\pi]$.

A

$\cfrac{\pi^2}{8}-\cfrac{\sin^2(\pi^2)}{8\pi^2}$

B

$\cfrac{\pi^2}{8}-\cfrac{\cos^2(\pi^2)}{8\pi^2}$

C

$\cfrac{\pi}{16}+\cfrac{\sin^2(\pi^2)}{16\pi^2}$

D

$\cfrac{\pi}{16}-\cfrac{\sin^2(2\pi^2)}{8\pi^2}$

E

$\cfrac{\pi^2}{8}+\cfrac{\cos^2(2\pi^2)}{16\pi^2}$