# Homework Help: Double integral over region surrounded by two ellipses

1. Apr 14, 2012

### pandarean

1. The problem statement, all variables and given/known data

A thin plate has the form of the intersection of the regions limited by $\frac{x^2}{9}$ + $\frac{y^2}{4}$ = 1 and $\frac{x^2}{4}$ + $\frac{y^2}{9}$ = 1

Which is the plate's mass if his density is δ(x, y) = |x|

2. The attempt at a solution

I've tried using u, v substitution

u = $\frac{x^2}{4}$ + $\frac{y^2}{9}$

v = $\frac{x^2}{9}$ + $\frac{y^2}{4}$

The resulting region looks nice, but the Jacobian is the ugly thing... i'm stuck.

I don't think polar is the way to go, one ellipse becomes a nice circle, but the other one becomes another ellipse....

Can someone give me some advice?
Thanks