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**1. The problem statement, all variables and given/known data**

**2. Relevant equations**

**3. The attempt at a solution**

Umm what just happened?

I understand as far as u=x+y and v = y/x and when he does the 2d curl. What I don't get is the step thereafter when he flips it. How does he know to flip it? Further, when he flips it wouldn't that make the dvdu inside the integral cancel and hence leave him with dxdy?