Set up, but do not evaluate, the integral which gives the volume when the region bounded by the curves y = Ln(x), y = 2, and x = 1 is revolved around the line y = −2.

Answer 1

you can do this as shells or washers.

with shells of thickness dy, remember that the volume of a shell is 2πrh. So, draw the region, and

∫[0,2] 2πrh dy

For discs with holes, of thickness dx, work with

∫[1,2] π(R^2-r^2) dx

your job is to examine the region in question and figure out R,r,h as required.

Answer 2

Ugh Steve why