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## Multivariable calculus

### Course: Multivariable calculus>Unit 4

Lesson 5: Double integrals

# Double integrals 2

Figuring out the volume under z=xy^2. Created by Sal Khan.

## Want to join the conversation?

• is there a better version of the video? its quite blurry.. thank you
• Why don't they use partial notation when sal writes dy and dx. Since it is a multivariable function, shouldn't you write partial x partial y?
• Because it is used for integrating. The dy and dx are just delta x and y from the limit form of integration.
(1 vote)
• what would have happened if you did dy first and then dx. It should be the same shouldn't it. int (0,2) int(0,1)xy^2dydx
• It will be the same - prove it to yourself - do it dydx
• Suppose we have a function f(x,y); when is the double integral of f(x,y)dxdy not equal to the double integral of f(x,y)dydx??
• It's possible that one is solvable, and the other is not. Other than that case, I'm pretty sure they are always equal. Especially in this context, where we are using the double integral to calculate volume under a curve, there would be a problem if the two double integrals were not equal, since that would imply there are two different volumes under f(x,y).
• Those drawings look like Picassos.
• Can anyone suggest some good books on curve sketching for a multivariable function?
• You use software like matlab or maple to sketch the function. Usually you wont be asked to sketch the function.
• If we are doing indefinite double integrals, do we have to add a constant of integration "C" like what we did in indefinite single integrals?