# Need help with integral

• March 23rd 2010, 10:24 PM
physicalpsychics
Need help with integral
Whole question:

Compute the area of the part of the surface $z = x^2 - y^2$ between the cylinders $x^2 + y^2 = 1$ and $x^2 + y^2 = 2.$

I've done the work to come up with the integral of

$
\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...
• March 23rd 2010, 10:54 PM
Haven
Convert to cylindrical coordinates.
$x = r \cos{t}$
$y = r \sin{t}$
$z = z$

but keep in mind that $dydx$ becomes $rdrd\theta$