Question

Find the volume of a solid by rotating the region bounded by the given curves about the specified line:
xy=1, y=0, x=1, x=2; about x=-1

Answer 1

I think method of shells would work here, integrating dx as thickness of shell.

Answer 2

I got that far, but I don't know what to set as the radii

Answer 3

Since the axis of rotation is at x=-1, the radius will be 1+x. Drawing a quick sketch of the curve and the boundaries makes it easier to see.

Answer 4

The generic differential volume would be dV=2π*r*y*dx
r=(1+x), y = 1/x. Integrate between 1 and 2 and that should do it.
I'm a little rusty at these, so I might be off somewhere.