This video shows an example of using Green's Theorem to simplify a line integral. The line integral is calculated the standard way and then Green's Theorem is applied as a comparison of difficulty.
This is part of a tutorial series on Vector Calculus that I made while an undergrad student that were recently unearthed. They are a bit old, so forgive me for the audio quality. I did clean it up a bit using Davinci Resolve Fairflight.
They were part of a website I had at the time that I always regretted taking down. I've since replaced it with a new one - markcwatson.dev - where I will put some of this old content.
https://markcwatson.dev