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

question 65

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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Definitions:

Hydrophobic Molecules

Molecules that repel water, typically nonpolar substances that do not mix with water.

Water

A transparent, tasteless, odorless, and nearly colorless chemical substance that is the main constituent of Earth's streams, lakes, and oceans, and the fluids of most living organisms.

Second Energy Level

The energy level beyond the first in an atom where electrons can reside, typically holding up to eight electrons.

Electrons

Subatomic particles with a negative charge, orbiting the nucleus of an atom and involved in chemical bonds and electrical current.