Finding the circulation and the outward flux across the boundary of a given region

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Given: (, ) = 〈ln(2 + 2), arctan(y/x)〉

where R is the annulus {(, }: 1 ≤ ⁡ ≤ 2⁡, 0⁡ ≤ ⁡ ≤ 2.

compute for the circulation and outward flux across the boundary of the given region.

The first thing I know is to use the normal form for the outward flux and tangential flux for the circulation. But what do you do with the region R? thank you.