Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C.
-$\mathbf { F } = \left( - \mathrm { y } - \mathrm { e } ^ { \mathrm { y } } \cos \mathrm { x } \right) \mathbf { i } + \left( \mathrm { y } - \mathrm { e } ^ { \mathrm { y } } \sin \mathrm { x } \right) \mathrm { j } ; \mathrm { C }$ is the right lobe of the lemniscate $\mathrm { r } ^ { 2 } = \cos 2 \theta$ that lies in the first quadrant.
A) $\frac { 1 } { 4 }$
B) 1
C) 0
D) $\frac { 1 } { 2 }$

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The Answer of Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C.
-$\mathbf { F } = \left( - \mathrm { y } - \mathrm { e } ^ { \mathrm { y } } \cos \mathrm { x } \right) \mathbf { i } + \left( \mathrm { y } - \mathrm { e } ^ { \mathrm { y } } \sin \mathrm { x } \right) \mathrm { j } ; \mathrm { C }$ is the right lobe of the lemniscate $\mathrm { r } ^ { 2 } = \cos 2 \theta$ that lies in the first quadrant.
A) $\frac { 1 } { 4 }$
B) 1
C) 0
D) $\frac { 1 } { 2 }$

Using Green's Theorem, Compute the Counterclockwise Circulation of F Around