Find the Flux of the Curl of Field F Through

Multiple Choice

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

A) $- 16 \pi$
B) 16
C) $- 16$
D) $24 \pi$