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

question 14

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

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