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

Multiple Choice

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

A) 0
B) 110
C) -10
D) 73