Use a CAS Integration Utility to Evaluate the Triple Integral

question 320

Multiple Choice

Use a CAS integration utility to evaluate the triple integral of the given function over the specified solid region.
- $F ( x , y , z ) = \frac { 1 } { \left( x ^ { 2 } + 2 \right) ^ { 3 / 2 } \left( y ^ { 2 } + 2 \right) ^ { 5 / 2 } \left( z ^ { 2 } + 2 \right) ^ { 7 / 2 } }$ over the rectangular cube $0 \leq x , y , z \leq 1$

• A) \(\frac { 1 } { 432 } \sqrt { 3 }\)
• B) \(\frac { 1 } { 864 } \sqrt { 3 }\)
• C) \(\frac { 1 } { 810 } \sqrt { 3 }\)
• D) \(\frac { 1 } { 630 } \sqrt { 3 }\)

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Definitions:

Regeneration

The process of renewal, restoration, and growth that makes genomes, cells, organisms, and ecosystems resilient to natural fluctuations or events that cause disturbance or damage.

Replacement

In biology, often refers to the substitution or restoration of cells, tissues, or organs.

Necrosis

Necrosis is the process of cell death which occurs as a result of disease, injury, or failure of the blood supply, often leading to tissue damage.

Connective Tissue

A type of biological tissue with an abundance of extracellular matrix that supports, binds together, and protects tissues and organs of the body.