Using Green's Theorem, Find the Outward Flux of F Across

Multiple Choice

Using Green's Theorem, find the outward flux of F across the closed curve C.
- $\mathbf { F } = \left( - \mathrm { y } - \mathrm { e } ^ { \mathrm { y } } \cos \mathrm { x } \right) \mathbf { i } + \left( \mathrm { y } - \mathrm { e } ^ { \mathrm { y } } \sin \mathrm { x } \right) \mathbf { j } ; \mathrm { C }$ is the right lobe of the lemniscate $\mathrm { r } ^ { 2 } = \cos 2 \theta$ that lies in the first quadrant.

A) $\frac { 1 } { 2 }$
B) $\frac { 1 } { 4 }$
C) 1
D) 0