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:

U.S. Euthanasia Society

A former organization in the United States that advocated for the legalization and ethical practice of euthanasia, aiming to provide information and support regarding end-of-life options.

Hemlock Society

An organization in the United States that supported active euthanasia and is presently the organization Compassion & Choices.

Voluntary Euthanasia Society

An organization that advocates for the rights of individuals to choose a dignified death, often in cases of terminal illness or severe suffering.

Mercy Killing

The act of killing someone painlessly, especially to relieve suffering from an incurable illness, also known as euthanasia.