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.
- $\mathbf { F } = 7 \mathrm { yi } - 5 \mathrm { z } \mathbf { j } - 5 \mathrm { x } \mathbf { k } ; \mathrm { S } : \mathbf { r } ( \mathrm { r } , \theta ) = \mathrm { r } \cos \theta \mathbf { i } + \mathrm { r } \sin \theta \mathbf { j } + \left( 36 - \mathrm { r } ^ { 2 } \right) \mathbf { k } , 0 \leq \mathrm { r } \leq 6$ and $0 \leq \theta \leq 2 \pi$

A) $252 \pi$
B) $- 252 \pi$
C) $- 252$
D) $- 42 \pi$