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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[@sarahfothergill8309]

I learn more from your videos than from lectures.

[@JohnnyV920]

nigga's handwriting is beautiful

[@james3440]

You sound like an idiot

[@jessenthebenezer]

@@james3440 six years ago fam

[@mohammadjadallah9813]

@@jessenthebenezer4 years ago fam

[@lynettemojica6503]

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

[@dezzylewis1025]

did you graduate yet

[@ashutoshraushan81]

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

[@azejlo90]

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

[@MisterTutor2010]

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.

[@fitrahazizah7267]

MisterTutor2010 yes if the curl of the field is zero, the field is conservative so the closed line integral equals zero

[@PhatPhunkyPhatso]

So comprehensive! You rock Sal :)

[@user-tc6uv5xh4s]

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

[@ayodeleesan8800]

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

[@rajatgoramba5642]

I found this 19 minutes before my exam. 🤦🏾‍♂️

[@Shelobes]

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

[@Ghaiyst]

Damn! I'm going to have a lot of fun in calculus 3 I bet. I'm starting at calculus 1 with calculus 2 readiness.

[@jkli6031]

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

[@CaptKarrot]

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

[@MuhammadAzzam92]

OMG thanks a lot dude!!!

[@trollfootballgeneration8645]

I was so obsessed with intuition that the actual integral process confused me lol..

[@SeanHampson]

Excellent Example/Tutorial

[@kellymoon3406]

Thank you so much, helped me alot.

[@beshtn4812]

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

[@Waranle]

Thanx Sal

[@cronus3675]

Finally found the best channel ❤️❤️ thank @khanacademy

[@BoxCarBoy12]

YOU ARE MAGIC, THANK YOU!!

[@hohodsj]

Thank you so much!!! you explain so well

[@yli5531]

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.

[@belalakaperal]

@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.

[@Justin37478]

Is there like a starting point to figure out what all this means? >.>

[@sherllymentalism4756]

Justin Baumann regular calculus

[@bjrntimotej5516]

@C i might help others reading it and having the same question ;)

[@thoughtyness]

So Justin, did you drop out or pass?

[@GOODBOY-vt1cf]

thank you so much

[@jzrobertjz]

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

[@derrickchikalekale8270]

Very helpful for me, thanks

[@bhaveshohal3390]

Beatifully explained......Cheers

[@chaitrasdp5606]

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

[@hohodsj]

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

[@juanpablodt]

Thank you very much.

[@baderabutaleb5475]

I love you khan

[@IifeIsgood]

thanks a lot!

[@voicefrompoland4493]

Great with one exception, the plot for the 2x^2 should be horizontal for x = 0

[@fourier07able]

VoiceFrom Poland : indeed you mean the tangent line at the origin (0,0) (y=2x^2, a parable passing for the origin) is horizontal. In fact the slope y'(x)=4x is zero at x=0, i.e. y'(0)=0. Also y''(x)=4 for all x, hence y''(0)=4>0, indicating a minimum at the origin for this parable which is convex.

[@aneeshalekshmibs7708]

i love this lecture 😘

[@efilnow]

good example

[@LINGFERNANDO]

Great! Thanks a lot, Khan~~

[@zisun8544]

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

[@FastTess]

brilliant!

[@power5able]

thank youu

[@dharanidharan1257]

subscribed with fulfilment... :)

[@gauripradhan8510]

Thank u :)

[@LookAtThatBigNameYo]

amazing.glad i subbed !

[@BenOrJed]

dudes.. what does the result represent? (16/15). is it the sum of the vectors within the region, is it an area, or a volume? WHAT???

[@dekuoldit244]

area

[@ANavya-sy3ls]

Can we verify this by line integral?

[@nlol2173]

ليه العرب ما يترجمون مثل هالمقاطع 💔

[@amrutrajpaunikar599]

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?

[@altuber99_athlete]

Components of the same.

[@zaeemameer8701]

5:18 shouldn't it be dx, tho he correct led it later

[@Jakers2009]

sal do u do these off the cuff?

[@petuncha]

I made the same mistake near the end!

[@mahnoorrahim1809]

I M SOO FUSTRATED EVERY EXAMPLE i encountered with is having different points i need same poiny examples like (1,0) (1,1)

[@dennercassio]

yolo ami I recommend you to go to the patricks channel . He does some exemples you want to know about

[@SaruwatariKaitoKun]

thanks a lot....ur better than my math prof. My prof has an accent, which was fun at first but now it just makes me sleepy.

[@andernaugle8962]

Can this be used to find the area of a country? Or is there another, more proficient way. (I’m looking to calculate the area of a country by hand for my calculus project)

[@monsieurLDN]

What are your known values?

[@metargel3066]

מעולה

[@dempAAAAAA]

Did you mean dx instead of da? 5:17

[@jasra1234]

dempAAAAAA no that’s by mistake

[@saurabhmittal6947]

sir, display sahi nahi h

[@Nikifuj908]

Sal, man, I love you- but brackets around your integrands!

[@andrewciricillo9726]

Thank you Mister Doctor Professor Khan it's ok ur the bad guy from star trek i forgive you papa bless

[@ownedncut]

awesome pics looking great thick solid tight thanks for the motivation.

[@rogueterror]

thank's a lot !