I have the following line integral in $\mathbb{R}^2$ $$ \int_C \left(\frac{\partial f}{\partial x} dx - \frac{\partial f}{\partial y} dy\right) $$ for a (known) piece-wise smooth curve $C$, and a (known) differentiable function $f$. Can anything be said, in general, about such an integral?
2026-03-25 03:07:16.1774408036
Anti-symmetric line integral
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