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**Tekken** $\displaystyle \int_{C}[f(x,y)dy - g(x,y)dx] = \int_{A}\int[\frac{\partial f}{\partial x} , \frac{\partial g}{\partial {y}}] dA $

Im trying to verify this theorem for the following line integral

$\displaystyle \int_{C}(x + y^{2})dy + (xy^{2}-y)dx $ where $\displaystyle C $ is the triangle with vertices $\displaystyle (1,1), (3,1), (3,3) $

I had no problem calculating the right hand side of green's theorem. However im struggling on the left hand side of the theorem.

Im thinking i need to get the line integral in terms of either x or y only ...?