Using Green's Theorem, Compute the Counterclockwise Circulation of F Around $\mathbf { F } = \sin 5 y \mathbf { i } + \cos 7 x \mathbf { j } ; \mathrm { C }$

Multiple Choice

Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C.
- $\mathbf { F } = \sin 5 y \mathbf { i } + \cos 7 x \mathbf { j } ; \mathrm { C }$ is the rectangle with vertices at $( 0,0 ) , \left( \frac { \pi } { 7 } , 0 \right) , \left( \frac { \pi } { 7 } , \frac { \pi } { 5 } \right)$ , and $\left( 0 , \frac { \pi } { 5 } \right)$

A) $- \frac { 2 } { 5 } \pi$
B) $- \frac { 4 } { 5 } \pi$
C) $\frac { 2 } { 5 } \pi$
D) 0