Use a Computer Algebra System to Compute the Flux Of \mathbf

question 48

Multiple Choice

Use a computer algebra system to compute the flux of $\mathbf { F }$ across $S . S$ is the surface of the cube cut from the first octant by the planes
$x = \frac { \pi } { 2 } , y = \frac { \pi } { 2 } , z = \frac { \pi } { 2 }$
$$\mathbf { F } ( x , y , z ) = 5 \sin x \cos ^ { 2 } y \mathbf { i } + 5 \sin ^ { 3 } y \cos ^ { 4 } z \mathbf { j } + 5 \sin ^ { 5 } z \cos ^ { 6 } x \mathbf { k }$$

• A) \(5 \pi ^ { 2 }\)
• B) \(95 \pi ^ { 2 }\)
• C) \(\frac { 5 \pi ^ { 2 } } { 64 }\)
• D) \(\frac { 95 \pi ^ { 2 } } { 64 }\)
• E) \(\frac { 95 \pi ^ { 2 } } { 32 }\)

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A calculation used in statistics and gambling to determine the average outcome of a series of random events, taking into account all possible scenarios and their probabilities.

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