Find the Flux of the Curl of Field F Through $\mathbf { F } = - 7 \mathrm { zi } + 6 x \mathbf { j } + 4 y \mathbf { k } ; S$

Multiple Choice

Find the flux of the curl of field F through the shell S.
- $\mathbf { F } = - 7 \mathrm { zi } + 6 x \mathbf { j } + 4 y \mathbf { k } ; S$ is the portion of the cone $z = 6 \sqrt { x ^ { 2 } + y ^ { 2 } }$ below the plane $z = 2$

A) $- \frac { 2 } { 3 } \pi$
B) $\frac { 4 } { 3 } \pi$
C) $- \frac { 1 } { 3 } \pi$
D) $- \frac { 4 } { 3 } \pi$