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[]{1-x^{2}}}^{\sqrt[]{2-x^{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...