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In this video, we use Stokes' theorem to give a quick proof of the path independence of line integrals for conservative vector fields. We also offer more discussion of conservative vector fields and simply connected regions. If you liked the video, please like the video, and if you want to see more of this type of content, consider subscribing! If you have any questions or video suggestions, post them in the comments section down below! 👍 To support the channel, hit the like button and subscribe. 🐸 To learn how I make these animations using Grant Sanderson's (3Blue1Brown) program Manim, check out my quick intro to Manim on Skillshare: https://www.skillshare.com/r/profile/... 🎸 Music in this video is from Epidemic Sound: https://www.epidemicsound.com/referra... Ways to support the channel: 🏆 Support the channel over on Patreon / kylebroder 🐸 Support the channel by signing up to a free trial of Skillshare using the link https://www.skillshare.com/r/profile/... FYI, these are affiliate links 💪🙏 These videos are separate from my research and teaching roles at the Australian National University, University of Sydney, and Beijing University. These videos are made using the open-source library -- Manim -- created by 3blue1brown: https://github.com/3b1b/manim