$D=\{(x,y)|5x^2+6y^2\leq1\}$
$\int\int_D \frac{x^2}{(5x^2+6y^2)^\frac3 2}$
The integrand is not bounded. When performing a polar transformation for the ellipse domain the integrand becomes bounded since the Jacobean is $\frac{1}{\sqrt40}r$:
$\frac{1}{\sqrt 40} cos^2(\theta)$
I was wondering what is the reason for that and if there is an intuitive way of understanding this transformation.