Green's Theorem

Applying Green's Theorem: An Example Problem
In this video, we apply Green's Theorem to evaluate a line integral over a given curve. You'll see how this powerful theorem connects a line integral around a simple closed curve to a double integral over the region enclosed by the curve. This example provides a step-by-step walkthrough to help you master the use of Green's Theorem in vector calculus.

What You Will Learn
How to apply Green's Theorem to a line integral.
How to set up the double integral over a region enclosed by a curve.
Step-by-step process of transforming a line integral into a double integral using Green's Theorem.
Techniques for evaluating the resulting double integral.
Green's Theorem is a fundamental tool in vector calculus that allows you to relate a line integral around a closed curve to a double integral over the region bounded by the curve. In this tutorial, we work through a specific example involving a triangular path and break down each step, from setting up the line integral to evaluating the double integral. This will deepen your understanding of the theorem and its applications in solving vector calculus problems.

If you find this video useful, please like, comment, and subscribe! Share this video with anyone studying vector calculus or needing help with Green's Theorem.

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[photon]

nearly 10 years later, this guy's videos are still helping thousands of students!

[Zikerrock]

Finals in one hour. Good luck fellow finalists.

[yiweizhang]

I WILL WATCH EVERY LAST VIDEO ON YOUR CHANNEL AND PASS CALC 3

[patrickjmt]

my pleasure, glad you like the videos

[AmusementLabs]

Lol, I'm getting all those "are those math videos from 2006 really helping? (Give us money)".
Well this is PatrickJMT so yes the videos are helping...

[pineappleking]

I'm currently in class while the teacher is teaching green theorem, and watching you teach it. Not only did my teacher misspell 'theorem' with two m's and no e's, he's only ever said about 3 sentences the entire class and mumbles to himself, Amazing videos man. Your really helping an massive amount of people.

[pauloricmp]

Thanks Patrick! You saved me once on Calculus I and now you're saving me again on Calculus II. Regards from Brazil.

[hzkzg]

I feel so relieved for someone telling me and me understanding what that circle on integral sign is. Thank you

[majsgo]

Patrick, your videos help me so much!! Thank you so much! I was wondering if you could do a video on stoke's theorem and on the divergens theorem? :) 

[patrickjmt]

oh... there is much left.
i have about 500, off the top of my head, that i would like to do.
more stats, linear algebra, differential equations, rest of multivariable calculus, more discrete math, more geometry....
lots to go

[Onedarkandwindynight]

Purely as a matter of interest, I live less than a quarter of a mile from Green's Mill in Sneinton, Nottingham (I can see t from my garden) Richard Green inherited the mill from his father and worked the mill full time. During whatever sparetime he could find he produced his famous theorems. He is buried in St Stephens, the local church.Greens Mill was renovated into a working windmill and interactive science centre by Nottingham University and actually grinds wheat which you can buy.

[SlurmzMKenzie]

You're the best Patrick! I'm in Calculus three and have my final tomorrow! You have helped me through all of Calculus. I will be donating in the near future!

[robynamegashie]

I know this video is like 2009 and we're in 2017 but it is helpful. but can you make a quick video on STOKE's theorem and divergence theorem before next week?

[Adavan]

Thanks so much for all your videos! You're making my life so much easier. It's really hard to understand college math professors sometimes, so it's awesome to have this as an additional resource.

[unclecelery]

not very helpful, it's extremely helpful

[theren]

Hey Mr. Patrick. Thank you for the assistance through out the semester. Completed my last problem paper for the semester, on Green's theorem. Now it's time to prepare for finals in about 2 weeks.
Thanks again.

One Love.

[AK-gtzy]

Thanks! Can you please make more Calc 3 videos? I'm finding it very hard without your guidance on some of these concepts.

[advikswamy]

I've been watching your videos for a few years now and I dunno if you'll ever see this but you've had a significant positive impact on my life ❤️🌸✨

[rehamkcirtap]

I use the circle on the integral symbol and the C under it to indicate a line integral around a closed curve. I also add a little arrow in to remind me of the direction. I'm not sure if it is a standard notation or not, but it helps me.

[md-kkob]

yeah patrick please do videos on stokes theorem and the divergence theorem