Find the Flux of the Vector Field F Across the Surface

Multiple Choice

Find the flux of the vector field F across the surface S in the indicated direction.
- $\mathbf { F } = 2 \mathrm { x } ^ { 2 } \mathrm { j } - \mathrm { z } ^ { 3 } \mathrm { k } ; \mathrm { S }$ is the portion of the parabolic cylinder $\mathrm { y } = 2 \mathrm { x } ^ { 2 }$ for which $0 \leq \mathrm { z } \leq 1$ and $- 1 \leq \mathrm { x } \leq 1$ ; direction is outward (away from the $y - z$ plane)

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