Green's theorem example 1 | Multivariable Calculus | Khan Academy

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Using Green's Theorem to solve a line integral of a vector field

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Multivariable Calculus on Khan Academy: Think calculus. Then think algebra II and working with two variables in a single equation. Now generalize and combine these two mathematical concepts, and you begin to see some of what Multivariable calculus entails, only now include multi dimensional thinking. Typical concepts or operations may include: limits and continuity, partial differentiation, multiple integration, scalar functions, and fundamental theorem of calculus in multiple dimensions.

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I learn more from your videos than from lectures. <3

sarahfothergill
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Now that classes are online due to the pandemic, I need these videos more than ever! Thank you!

lynettemojica
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Best teacher, finally I m comfortable in this topic, thank u sir

ashutoshraushan
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loved your video, great work, wanna meet you from karachi, Pakistan 😘😘😘😘😘😘😘😘😘😘

Abdul-bj
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If the field is conservative it does not matter whether you go clockwise or counter clockwise since the closed line integral equals zero for a conservative field.

I originally subbed for the video on diff eq so I could understand quantum mechanics better. The calculus playlist is just as interesting.

MisterTutor
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Integral over the boundary of C with f = integral over C with df
where f is an exterior n form d denoted the exterior covariant differential

jkli
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Be carful!, you difened R containing the border ( use >= instead of just >).
Your videos are very helpful, congratulations!

Shelobes
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last minute before the exam O.M.G! thank you so much!

CaptKarrot
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Finally found the best channel ❤️❤️ thank @khanacademy

cronus
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Wow. I only had to take Finite Math and Business Calculus for my major. Still, I'm watching this video because it amazes me just how much further math goes. This is like a foreign language to me, but it's cool to see this stuff even if I don't get A THING. haha

azejlo
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Thank you so much!!! you explain so well

hohodsj
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I have one doubt!! greens theorem in multivariable calculus or green function in multivariable calculus which one is correct??

chaitrasdp
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Strictly speaking, the two crossing points are not smooth so the assumption of your previous Green's theorem is not satisfied. But it doesn't hurt because the spikes are of measure 0.

yli
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Could I took 2x^2 as upper limit and 2x lower limit?

zisun
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it's the area of that small region between 2x and 2x^2...

jzrobertjz
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gosh I should have watched this first! I wasted hours on this topic >_< !!!! Best video!

beshtn
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@BenOrJed If the vector field is a force field it represents the work done on an object by that field, besides that, I have no idea.

belalakaperal
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It took me months to discover this hidden treasure here. Not too late though

ayodeleesan
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can you do a lecture on Tangential and Normal Component of Acceleration?

hohodsj
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i have a doubt. two variables 'P(x, y)' and 'Q(x, y)' are they two completely different vectors or are they components of same vector?

amrutrajpaunikar