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.
- $\mathrm { F } = \mathrm { x } ^ { 5 } \mathrm { y } ^ { 2 } \mathrm { i } + \mathrm { yj } - \mathrm { zk } ; \mathrm { S }$ is the portion of the parabolic cylinder $\mathrm { z } = 4 - \mathrm { y } ^ { 2 }$ for which $\mathrm { z } \geq 0$ and $2 \leq \mathrm { x } \leq 10$ ; direction is outward (away from the $x$ -y plane)

A) -128
B) 128
C) 0
D) 64