Multiple Integrals 12: Double Integrals in Polar Coordinates

[browno26]

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[browno26]

thanks donnylee

[krustygerbil]

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[browno26]

@krustygerbil what a stupid comment

[krustygerbil]

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[browno26]

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[krustygerbil]

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[browno26]

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[krustygerbil]

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[flukeekulf]

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[ClickMe2c]

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[nevergoaway1]

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[debunker1905]

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[fermixx]

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by the way, nice video, your graphs are outstanding !

[xDuoSx]

This is something what my so called PhD profs could never teach me, but you made it so much easier to understand. Thx!

[alcideslugo]

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[dizzydjuggalo]

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[illusion422]

Another method would be to use the Jacobian, I believe students have already learned partial derivation if they are solving double integrals.

x = r cos(theta) , y = r sin(theta)

J = |del(x)/del(r) del(x)/del(theta)| |del(y)/del(r) del(y)/del(theta)|

This is the determinant of the partial derivatives.

|cos(theta) -r sin(theta)|

|sin(theta) r cos(theta) |

r cos^2(theta) + r sin^2(theta) = r = Jacobian.

So dA becomes r dr d(theta)

[LongShlong125]

damm I didn't study single variable integrals with polar coordinates too much so I still don't get it that well...

[donylee]

Hey LongShiong,

Trying to sound as humble as possible, I can see that you like my videos as you have been commenting on almost all of them in the 'Multiple Integrals' series thus far.

Do hope you learn something from them though. Thanks for watching!

[krustygerbil]

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