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.
- $$\mathbf { F } = \ln \left( x ^ { 2 } + y ^ { 2 } \right) i + \tan ^ { - 1 } \left( \frac { x } { y } \right) ; \quad C \text { is the region defined by the polar coordinate inequalities } 3 \leq r \leq 6 \text { and } 0 \leq \theta \leq \pi$$

A) 27
B) 45
C) 0
D) 54