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

question 66

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
$$\begin{array} { l } x = \frac { \pi } { 2 } , y = \frac { \pi } { 2 } , z = \frac { \pi } { 2 } \\\mathbf { F } ( x , y , z ) = 3 \sin x \cos ^ { 2 } y \mathbf { i } + 3 \sin ^ { 3 } y \cos ^ { 4 } z \mathbf { j } + 3 \sin ^ { 5 } z \cos ^ { 6 } x \mathbf { k }\end{array}$$
Select the correct answer.

• A) \(\frac { 3 \pi ^ { 2 } } { 64 }\)
• B) \(\frac { 57 \pi ^ { 2 } } { 64 }\)
• C) \(57 \pi ^ { 2 }\)
• D) \(\frac { 57 \pi ^ { 2 } } { 32 }\)
• E) \(3 \pi ^ { 2 }\)

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Definitions:

Gastrocnemius

A large muscle located in the back part of the lower leg, forming part of the calf and responsible for flexing the foot and bending the knee.

Orbicularis Oculi

A circular muscle around the eye socket that allows for the closing of the eyes.

Gluteus Maximus

The largest and most superficial of the three gluteal muscles, significantly involved in the movement and stability of the hip and thigh.

Posterior Thigh

The posterior thigh refers to the back part of the thigh, encompassing the muscles, nerves, and tissues located behind the femur, primarily involved in the extension and rotation of the leg.