How do you use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by y=1/x, y=0, x=1, and x=2 about the y-axis?
Please see the explanation section, below.
Here is the region (blue) with a thin slice taken parallel to the axis of rotation. To set up for cylindrical shells. (The slice has black edges.)
The volume of a representative shell is
In this case, we have