
Need help with integral
Whole question:
Compute the area of the part of the surface $\displaystyle z = x^2  y^2$ between the cylinders $\displaystyle x^2 + y^2 = 1$ and $\displaystyle x^2 + y^2 = 2.$
I've done the work to come up with the integral of
$\displaystyle
\int_{1}^{2}\int_{\sqrt[]{1x^{2}}}^{\sqrt[]{2x^{2}}} \sqrt[]{4x^{2}+4y^{2}+1}dydx
$
and I'm not sure how to go about solving this. Trig sub? of what exactly? and then...

Convert to cylindrical coordinates.
$\displaystyle x = r \cos{t}$
$\displaystyle y = r \sin{t}$
$\displaystyle z = z$
but keep in mind that $\displaystyle dydx$ becomes $\displaystyle rdrd\theta$