Using Green's Theorem, Compute the Counterclockwise Circulation of F Around $F = - \frac { 1 } { 8 \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 4 } } \mathrm { i } ; \mathrm { C }$

Multiple Choice

Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C.
- $F = - \frac { 1 } { 8 \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 4 } } \mathrm { i } ; \mathrm { C }$ is the region defined by the polar coordinate inequalities $1 \leq \mathrm { r } \leq 3$ and $0 \leq \theta \leq \pi$

A) 0
B) $\frac { 4372 } { 15309 }$
C) $\frac { 4376 } { 15309 }$
D) $- \frac { 4372 } { 15309 }$