Find the Flux of the Curl of Field F Through

question 239

Multiple Choice

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

• A) \(- 24 \pi\)
• B) \(24 \pi\)
• C) \(- 12\)
• D) \(- 12 \pi\)

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Definitions:

Null Hypothesis

A statement in hypothesis testing that proposes no significant difference or effect, serving as the default assumption to be tested against.

Probability

A measure quantifying the likelihood that certain events will occur.

Null Hypothesis

Re-phrased: The presumption in statistical testing that asserts no association or effect among studied variables.

Critical Value

A threshold in hypothesis testing that defines the boundary beyond which an observed test statistic is considered statistically significant.