Using Green's Theorem, Find the Outward Flux of F Across $\mathrm { F } = - \frac { 1 } { 4 \left( \mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } \right) ^ { 2 } } \mathrm { i } ; \mathrm { C }$

Multiple Choice

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

A) $\frac { 7 } { 12 }$
B) $\frac { 7 } { 24 }$
C) $- \frac { 7 } { 12 }$
D) 0