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

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) $80 \pi$