Find the Flux of the Curl of Field F Through $\mathbf { F } = ( 4 - \mathrm { y } ) \mathbf { i } + ( 3 + \mathrm { x } ) \mathbf { j } + \mathrm { z } ^ { 5 } \mathbf { k } ; \mathrm { S }$

Multiple Choice

Find the flux of the curl of field F through the shell S.
- $\mathbf { F } = ( 4 - \mathrm { y } ) \mathbf { i } + ( 3 + \mathrm { x } ) \mathbf { j } + \mathrm { z } ^ { 5 } \mathbf { k } ; \mathrm { S }$ is the upper hemisphere of $\mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } + \mathrm { z } ^ { 2 } = 16$

A) $64 \pi$
B) $2 \pi$
C) $32 \pi$
D) $- 4 \pi$