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Multivariable Calculus

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Average Value Over a Region

MVCALC-VJIEDE

Calculate the average value of the following functions over the region $R$.

$$f(x,y) = 2\sin x \sin y; \quad R=\{(x,y): 0\leq x \leq \pi, 0\leq y\leq \pi\}$$

A

$\cfrac{1}{\pi^2}$

B

$\cfrac{8}{\pi^2}$

C

$0$

D

$1$

E

None of the above