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) \(3 \pi ^ { 2 }\)

Define and understand the impact of critical population density on genetic diversity and species survival.

Understand the historical context of species extinction and efforts for conservation.

Understand the role of human activities in the current extinction crisis.

Identify conservation efforts and laws aimed at protecting wildlife.