Green's Theorem
Table of Contents
If \(\small P\) and \(\small Q\) are continuous functions of \(\small x\) and \(\small y\) over the region \(\small D\) with a closed path \(\small C\) that bounds \(\small D\), then Green’s theorem states that
$$ \oint_C Pdx + Qdy = \iint_D \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} dA $$
Honestly, just read Paul’s Online Notes, they’re great.
Green’s theorem can be thought of as a 2D version of Stokes’ theorem.