Calculate the Flow in the Field F Along the Path

Multiple Choice

Calculate the flow in the field F along the path C.
- $\mathbf { F } = ( \mathrm { x } - \mathrm { y } ) \mathbf { i } - \left( \mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } \right) \mathbf { j } ; \mathrm { C }$ is curve from $( 4,0 )$ to $( - 4,0 )$ on the upper half of the circle $\mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } = 16$

A) $8 \pi$
B) $- 8 \pi$
C) $\frac { 16 \pi - 1 } { 4 }$
D) $16 \pi$