There is the region bounded by y=ln x, y=0, x=1, and x=e.

I need the volume when this is revolved about y-axis.

This will be a washer...so I have that x=e^y and now I did.....

pi*integral (0 to 1) e^2-e^2y dy

Is this correct?

I put outer radius of e and inner of e^y...would that be correct?