This is not a homework problem this is just a problem I was thinking about whether or not it would be possible to solve without cylinderical shells The region bounded by y=1/(x^2) x=e x=e^3 and the x axis Rotated around y axis.. I did cylindrical shells and got 4pi and then wondered if I could do without. I have been trying to figure out how to do it for about an hour but cant come up with anything that works. Is it possible to do by hand without cylinderical shells? If so I would like so advice on how to go about it.