$\displaystyle y=2/x $

$\displaystyle y=0$

$\displaystyle x=1 $

$\displaystyle x=3$

Rotate about $\displaystyle y = -1$

Outside radius = $\displaystyle (-1-2/x)^2$

Inside radius = 1

$\displaystyle \int_1^3 ((-1-2/x)^2-1)dx = 22.1831495912$

Is this correct?

Thanks in advance