Green's theorem

It is sometimes easier to take a double integral (a particular double integral as we'll see) over a region and sometimes easier to take a line integral around the boundary. Green's theorem draws the connection between the two so we can go back and forth. This tutorial proves Green's theorem and then gives a few examples of using it. If you can take line integrals through vector fields, you're read

Simple, closed, connected, piecewise-smooth practice

Green's theorem proof (part 1)

Green's theorem proof (part 2)

Green's theorem example 1

Green's theorem example 2

Circulation form of Green's theorem