# Jacobian transformation integral

• Apr 24th 2013, 12:01 AM
mathlover10
Jacobian transformation integral
$\displaystyle \int \int x^2dA=6\pi....where 9x^2+4y^2=36, x=2u, y=3v$
ellipse is the 1st region.... there are theoretical proofs of the Jacobian transformation using vector analysis? (Happy)the higher powers of the Jacobian are used for general relativity
• Apr 24th 2013, 12:12 AM
chiro
Re: Jacobian transformation integral
Hey mathlover10.

Are you talking about the substitution theorems for multi-variable calculus?
• Apr 24th 2013, 01:11 AM
Prove It
Re: Jacobian transformation integral
Quote:

Originally Posted by mathlover10
$\displaystyle \int \int x^2dA=6\pi....where 9x^2+4y^2=36, x=2u, y=3v$
ellipse is the 1st region.... there are theoretical proofs of the Jacobian transformation using vector analysis? (Happy)the higher powers of the Jacobian are used for general relativity

I'm not sure what you're asking. Are you asking to actually evaluate this double integral using the given transformation, or do you want more information about transformations and Jacobians in general?
• Apr 25th 2013, 11:04 PM
mathlover10
Re: Jacobian transformation integral
this is an easy integral you can do by inspection where u^2+v^2=1 and you can change to radial coordinates or use square root limits
I've worked through the proof of approximating the image region R by secant vectors in Stewart in change of variable integrals but was a little unclear...I've heard that Hubbard or others are good texts....but maybe it's better to spend time learning other things like complex analysis?....