You've reached the end of Multivariable Calculus! In this video we generalized the good old "usubs" of first year calculus to multivariable case with a multivariable change of variables. The trick is to set up a new coordinate system where the messy region before is now very nice, perhaps just a rectangle. We have to be careful though as we have to multiply our integrands by a scaling factors called the Jacobian. In this video I sketch the intuition behind the Jacobian and compute it out in an example.

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This video was created by Dr. Trefor Bazett. I'm an Assistant Teaching Professor at the University of Victoria.

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