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.
- $$\mathbf { F } = ( 4 \mathrm { y } + 2 ) \mathbf { i } - 5 \mathrm { xj } + \left( \mathrm { e } ^ { \mathrm { z } } - 1 \right) \mathbf { k } ; \mathrm { S } : \mathbf { r } ( \mathrm { r } , \theta ) = 2 \sin \varphi \cos \theta \mathbf { i } + 2 \sin \varphi \sin \theta \mathbf { j } + 2 \cos \varphi \mathbf { k } , 0 \leq \theta \leq 2 \pi \text { and } 0 \leq \varphi \leq \frac { \pi } { 2 }$$

A) 72
B) $- 72 \pi$
C) $- 36 \pi$
D) $36 \pi$