Use a CAS Integration Utility to Evaluate the Triple Integral $F ( x , y , z ) = \left( \frac { 1 } { \left( x ^ { 2 } + 4 \right) \left( y ^ { 2 } + 4 \right) \left( z ^ { 2 } + 4 \right) } \right) ^ { 3 / 2 }$

question 28

Multiple Choice

Use a CAS integration utility to evaluate the triple integral of the given function over the specified solid region.
- $F ( x , y , z ) = \left( \frac { 1 } { \left( x ^ { 2 } + 4 \right) \left( y ^ { 2 } + 4 \right) \left( z ^ { 2 } + 4 \right) } \right) ^ { 3 / 2 }$ over the rectangular cube $0 \leq x , y , z \leq 1$

• A) \(\frac { \sqrt { 5 } } { 8000 }\)
• B) \(\frac { \sqrt { 5 } } { 1600 }\)
• C) \(\frac { \sqrt { 5 } } { 2000 }\)
• D) \(\frac { \sqrt { 5 } } { 400 }\)

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Definitions:

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A period of delay or suspension of activity; in developmental psychology, it refers to a period where individuals are not making any significant decisions regarding their personal identity.

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The various configurations of identity development in adolescents and adults as theorized by psychologists, including stages of exploration and commitment.

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A state of physical or psychological ease, often free from pain or constraint.

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A sense of personal suitability to a particular profession or occupational category, often developed during adolescence.