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Find the Flux of the Curl of Field F Through

question 234

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Find the flux of the curl of field F through the shell S.
- F=x2yi3xy2j+lnzk;S:r(r,θ) =rcosθi+rsinθj+2rk,0r2\mathbf { F } = \mathrm { x } ^ { 2 } \mathrm { yi } - 3 x \mathrm { y } ^ { 2 } \mathbf { j } + \ln \mathrm { zk } ; \mathrm { S } : \mathrm { r } ( \mathrm { r } , \theta ) = \mathrm { r } \cos \theta \mathbf { i } + \mathrm { r } \sin \theta \mathbf { j } + 2 \mathrm { rk } , 0 \leq \mathrm { r } \leq 2 and 0θ2π0 \leq \theta \leq 2 \pi

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Definitions:

Stable Factors

Characteristics or elements that remain constant over time in a given context or system.

External

Pertaining to or situated on the outside of something; relating to the outer environment or surroundings.

Unstable

Lacking in stability, predictability, or consistency, often leading to unpredicted changes or outcomes.

Specific Factors

Elements or conditions that are distinct and contribute to a particular outcome or situation.

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