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# 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
• 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
• 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?
(1 vote)
• Yes, you will still need to add C. However, you will rarely end up doing indefinite integrals like this.
(1 vote)
• What program is he using to graph those surfaces?
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• Those drawings look like Picassos.
(1 vote)
• Can anyone suggest some good books on curve sketching for a multivariable function?
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• You use software like matlab or maple to sketch the function. Usually you wont be asked to sketch the function.
(1 vote)
• does the order of dx and dy matter I mean can we put dy before dx and evaluate the y integral first?
(1 vote)
• 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??
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• 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).
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• Should the ranges be different, would the sequence be different?
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• at , he said we consider y as constant, isn't y changing with x so that we must get the relation between them and substitute for y ? like in 2D?.....thanks in advance :)
(1 vote)
• for each of those frame environments in the x plane that the integral uses, y is a constant
(1 vote)