Find the Flux of the Curl of Field F Through $\mathrm { F } = - 5 \mathrm { x } ^ { 2 } \mathrm { yi } + 5 \mathrm { xy } ^2 \mathbf { j } + \mathrm { z } ^ { 5 } \mathbf { k }$

question 5

Multiple Choice

Find the flux of the curl of field F through the shell S.
- $\mathrm { F } = - 5 \mathrm { x } ^ { 2 } \mathrm { yi } + 5 \mathrm { xy } ^2 \mathbf { j } + \mathrm { z } ^ { 5 } \mathbf { k }$ ; $\mathrm { S }$ is the portion of the paraboloid $2 - \mathrm { x } ^ { 2 } - \mathrm { y } ^ { 2 } = \mathrm { z }$ that lies above the $x y -$ plane

• A) \(\frac { 40 } { 3 } \pi\)
• B) \(10 \pi\)
• C) 80
• D) \(80 \pi\)

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