Let And Let S Be the Boundary Surface of the Solid

question 97

Multiple Choice

Let $\mathbf { F } ( x , y , z ) = \left( x ^ { 3 } + y \sin z \right) \mathbf { i } + \left( y ^ { 3 } + z ^ { 2 } \sin z \right) \mathbf { j } + \left( z ^ { 3 } + x \right) \mathbf { k }$ and let S be the boundary surface of the solid E bounded by $z = \sqrt { 4 - x ^ { 2 } - y ^ { 2 } } , z = \sqrt { 1 - x ^ { 2 } - y ^ { 2 } }$ , and $z = 0$ . Evaluate the surface integral $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ .

• A) \(\frac { 62 \pi } { 5 }\)
• B) \(\frac { \pi } { 2 }\)
• C) \(\pi\)
• D) \(\frac { 4 \pi } { 3 }\)
• E) \(\frac { 2 \pi } { 3 }\)
• F) \(\frac { 192 \pi } { 5 }\)
• G) \(\frac { 186 \pi } { 5 }\)
• H) \(4 \pi\)

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Definitions:

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Psychological strategies that individuals use to manage stress, deal with traumatic events, or navigate difficult emotional circumstances.

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The body's response to any demand or challenge, which can be triggered by both positive and negative experiences.

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The principle that emphasizes fairness in the treatment of individuals and the provision of support to employees by organizations.