Green's theorem example 2 | Multivariable Calculus | Khan Academy

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Another example applying Green's Theorem

Missed the previous lesson?

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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If only you were my lecturer!!! Amazing job!

zerahgeorge
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This is absolutely fantastic! I am only in calculus 1, but I have borrowed my AP statistics teacher's calculus 1 and 2 college books to glance through and I have came across Stoke's Theorem and Green's Theorem. I always wanted to know how to work those out, thanks for the intuition Sal! You are my hero!

ZeusPeen
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My book has me doing it both ways for each problem fkn hell.

DanikonLUK
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i love you dude. gonna pass my exam tomorrow only cos of u LOL

Umair
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you must use the polar coordinates to solve this type of problems,
you are making an example here it is not always the case to take a full circle

AhdFOUR
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Thanks Sal! This really helped! I have an assignment that's making me do it both ways (with parameterisation and Green's Theorem).

calumblack
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please provide all the videos for linear algebra! please and thank you

remsenking
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Thanks Sal, always so helpful and clear as usual!

jyslakay
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Excellent. - Question: If in the examples you calculated a work done by a vector field - then, in the interpretation of the double integral... does (in numbers without units) the value of the line integral equals the value of the volume "created" by vector field and line...and is here 5 pi? Means... work equals volume (without units) in the number?

norwayte
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@Herber3 i agree. show us Stokes Theorem

alkalait
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Region to left,
Region to right,
Means?

jagsproduction
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what happens if instead of getting 5 after the operation I get : 2y-.3y^2  ? and the radio of the circle is 2.

yue
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The last part where you evaluate the double integral i did it with a parametrization with polar coordinates with R between 0 and 1 and the angle between 0 and 2 pi. I managed to get the same result tho I'm not sure if that's the way to go.

s.i.h
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thank you sir its really really help me.

muhdakhram
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Sad they didn't make a video for the flux/divergence form

isaacliu
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can you PLEASE do an example with parametric equations? Say like x=t^2 and y=t^3-5t? if you cant please respond quickly so i know what to do!

MegaNabz
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it will be more understandable if you solve both sides...🙂

nafeesatahir
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Hi nice video! What I don't understand well is, when do I know that I have to use the Greens Theorem?

shinable
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sal u had said earlier in the videos that double integral gives the volume and now you have written the area could you please clarify?

jaysonsequeira
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why is the double integral area and not volume?

luvley
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