You have a mistake in definition.
See this.
It should be
Consider x>=0 and 0<=y<=1/x.
Show that this has finite volume.
I get integral from 0 to infinity of 2pi*(1/x^2), but this does not converge because of the asymptote, right? I know it would converge, and so have finite volume, if I took 1 to infinity. On the other hand, when I do 0 to infinity, it diverges, right? Is this probably a typo on my sheet or am I doing something wrong