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.
- $$\mathrm { F } = - \sqrt { \mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } } \mathrm { i } + \sqrt { \mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } } \mathrm { j } ; \mathrm { C } \text { is the region defined by the polar coordinate inequalities } 9 \leq \mathrm { r } \leq 10 \text { and } 0 \leq \theta \leq \pi$$

A) 0
B) 181
C) 38
D) 10