Find the Average Value Of $f ( x , y , z ) = x ^ { 3 } + y ^ { 2 } + z ^ { 4 } \text { over the region } Q \text {, where } Q \text { is a }$

question 7

Multiple Choice

Find the average value of
$f ( x , y , z ) = x ^ { 3 } + y ^ { 2 } + z ^ { 4 } \text { over the region } Q \text {, where } Q \text { is a }$ cube in the first octant bounded by the coordinate planes, and the planes $x = 4 , y = 1$ , and $z = 2$ . The average value of a continuous function $f ( x , y , z )$ over a solid region $Q$ is $\frac{1}{V} \iiint_{Q} f(x, y, z) d V$ where $V$ is the volume of the solid region $Q$ .

• A) \(\frac { 293 } { 15 }\)
• B) \(\frac { 31 } { 586 }\)
• C) \(\frac { 293 } { 308 }\)
• D) \(\frac { 308 } { 293 }\)
• E) \(\frac { 15 } { 293 }\)

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