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

ninjacookies

I'm trying to evaluate the double integral

[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.

PowerWill

Converting to rectangular coordinates would probably be easier

PowerWill

That's cylindrical coordinates, sorry

hypermorphism

Answered in Calculus and Analysis.

ninjacookies

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

dextercioby

Please,DO NOT DOUBLE POST!!

Daniel.

PowerWill

Dexter...you need to drop the intensity down a notch. And to the ninja, just convert [tex] x^2 + y^2 [/tex] to [tex] r^2 [/tex] and integrate over the same area in cylindrical.

dextercioby

He can't do that,the square [0,1]*[0,1] is not equivalent to the quarter of the circle you're implying...

Daniel.