Find the Flux of the Curl of Field F Through

question 25

Multiple Choice

Find the flux of the curl of field F through the shell S.
- $\mathbf { F } = 7 \mathrm { yi } - 5 \mathrm { z } \mathbf { j } - 5 \mathrm { x } \mathbf { k } ; \mathrm { S } : \mathbf { r } ( \mathrm { r } , \theta ) = \mathrm { r } \cos \theta \mathbf { i } + \mathrm { r } \sin \theta \mathbf { j } + \left( 36 - \mathrm { r } ^ { 2 } \right) \mathbf { k } , 0 \leq \mathrm { r } \leq 6$ and $0 \leq \theta \leq 2 \pi$

• A) \(252 \pi\)
• B) \(- 252 \pi\)
• C) \(- 252\)
• D) \(- 42 \pi\)

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Definitions:

Validity

The extent to which a test, measure, or research accurately reflects or assesses the specific concept it is intended to.

Reliability

The degree to which an assessment tool or measurement can produce stable and consistent results over time.

Hypothesis

A proposed explanation made on the basis of limited evidence, serving as a starting point for further investigation.

Structuralism

A theoretical perspective in psychology that emphasizes understanding the structure of the mind by breaking it down into its component parts.