Chapter 14.4, Problem 40E

Circulation and flux For the following vector fields, compute (a) the circulation on and (b) the outward flux across the boundary of the given region, Assume boundary curves have counterclockwise orientation.

40.     $F=\langle \ln \left(x^2+y^2\right),{\tan }^{-1}\frac{y}{x}\rangle$, where R is the annulus $\left\{\left(r,\theta \right):1\le r\le 2,0\le \theta \le 2\pi \right\}$