# Math Help - Torricelli's trumpet

1. ## Torricelli's trumpet

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

It should be $x\ge 1.$