Review: Green's Theorem

Today, we formed tripods to work on a worksheet on Green's Theorem. The problems on it were straightforward with basic applications of the theorem, but for question 2a, I got a negative answer. Does anyone know why? Or got a different answer? Just a reminder, Green's Theorem is:

Let R be a simply-connected region (no holes; doesn't cross itself) with a piecewise smooth (differentiable everywhere) boundary C (continuous, with a finite number of cusps) with positive orientation (counter clockwise orientation). If P and Q have continuous partial derivatives, then