Use the Divergence Theorem to Calculate the Surface Integral $\iint _ { s } \mathbf { F } \cdot d \mathbf { S }$

question 32

Multiple Choice

Use the Divergence Theorem to calculate the surface integral $\iint _ { s } \mathbf { F } \cdot d \mathbf { S }$ ; that is, calculate the flux of $\mathbf { F }$ across $S$ .
$$\mathbf { F } ( x , y , z ) = x y e ^ { z } \mathbf { i } + x y ^ { 2 } z ^ { 3 } \mathbf { j } - y e ^ { z } \mathbf { k }$$
$S$ is the surface of the box bounded by the coordinate planes and the planes $x = 5 , y = 2$ and $z = 1$ .
Select the correct answer.

• A) \(\frac { 11 } { 3 }\)
• B) \(\frac { 25 } { 2 }\)
• C) \(\frac { 5 } { 3 }\)
• D) \(\frac { 2 } { 25 }\)
• E) \(\frac { 7 } { 3 }\)

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