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.
- $\mathbf { F } = - 5 \mathrm { zi } - 3 \times \mathbf { j } - 2 \mathrm { yk } ; \mathrm { S } : \mathrm { r } ( \mathrm { r } , \theta ) = \mathrm { r } \cos \theta \mathbf { i } + \mathrm { r } \sin \theta \mathbf { j } + 6 \mathrm { rk } , 0 \leq \mathrm { r } \leq 6$ and $0 \leq \theta \leq 2 \pi$

A) $- 108 \pi$
B) $- 108$
C) 0
D) $108 \pi$