Let R be the region bounded by the curve y = ln(x), the lines x = 1 and y = 2

(a) Find the volume of the solid obtained by rotating R around the line y = 3
(b) Find the volume of the solid obtained by rotating R around thine x = -1
(c) Find the volume of the solid with cross-sections perpendicular to the y-axis that are circles

Question

Let R be the region bounded by the curve y = ln(x), the lines x = 1 and y = 2

(a) Find the volume of the solid obtained by rotating R around the line y = 3
(b) Find the volume of the solid obtained by rotating R around thine x = -1
(c) Find the volume of the solid with cross-sections perpendicular to the y-axis that are circles

mathmale · Answer

Mind posting just one problem at a time?
I think it important for you to draw a graph of the given function y=ln x, as well as of the two boundary lines x=1 and y=2.  Next, draw the axis of rotation, y=3.

You'll need to select your method from among the following:
1.  Shells
2.  Washers
3.  Disks

Please experiment with the Draw utility (below), if you haven't already.
I may not respond right away, but if you still need help when I'm back on OpenStudy, i'd be glad to provide it.  Good luck!