Another quick please tell me if my logic seems correct (change of variables)

I'm trying to evaluate the double integral

$$\int \int \sqrt{x^2 + y^2} \, dA$$

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)

$$\int \int \sqrt{u + v} * (1) dudv$$

which resulted in a value of roughly 3.238.

Converting to rectangular coordinates would probably be easier

That's cylindrical coordinates, sorry

I'm totally at a loss here guys. I realized my Jacobian was computed wrong. Can someone please give me a clue as to what would be the most efficient integral setup? I'm completely dumbfounded. :( Thanks

edit: more in-depth post in the calculus forum, thanks

Last edited:
dextercioby
Homework Helper
Dexter...you need to drop the intensity down a notch. And to the ninja, just convert $$x^2 + y^2$$ to $$r^2$$ and integrate over the same area in cylindrical.