- #1

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[tex]\int \int \sqrt{x^2 + y^2} \, dA[/tex]

over the region R = [0,1] x [0,1]

using change of variables.

Well, after fooling around, I've got an answer. I set u = x^2, v =y^2, and then calculated the jacobian of T which was 1. The image transformation limits of integration for u and v turned out to be the same [0,1] x [0,1]

So I did the following calculation (both integrals going from 0 to 1)

[tex]\int \int \sqrt{u + v} * (1) dudv[/tex]

which resulted in a value of roughly 3.238.

Does my logic and answer seem sound here? Thanks in advance.