So given this curve: $$y=\sqrt{9x-18},\ \ 2 \le x \le 6$$
And using this lovely formula: $$\int2πy\sqrt{1+(\frac{dy}{dx})^2} dx$$
This is what I get for a set up:
$$\int_2^62π \sqrt{9x-18}\sqrt{(\frac{2x-3}{2x-24})} dx$$
I don't know, this set up is looks pretty weird. I think I screwed up when I was squaring (dy/dx).