Calculate the Flux of the Field F Across the Closed $\mathbf { F } = \mathrm { y } ^ { 2 } \mathbf { i } + \mathrm { x } ^ { 3 } \mathbf { j }$

Multiple Choice

Calculate the flux of the field F across the closed plane curve C.
- $\mathbf { F } = \mathrm { y } ^ { 2 } \mathbf { i } + \mathrm { x } ^ { 3 } \mathbf { j }$ ; the curve $\mathrm { C }$ is the closed counterclockwise path formed from the semicircle $\mathbf { r } ( \mathrm { t } ) = 3 \cos \mathrm { ti } + 3$ sin $\mathrm { j }$ , $0 \leq t \leq \pi$ , and the straight line segment from $( - 3,0 )$ to $( 3,0 )$

A) $= \frac { 27 } { 2 }$
B) 0
C) $\frac { 27 } { 2 }$
D) 27