01
Shells volume - offset graph,
-axis Consider the region in the first quadrant bounded by the lines
, , , and the curve . Revolve this about the -axis. Find the volume of the resulting solid.
02
Shells volume - set up integrals, both axes
Consider the region in the first quadrant bounded by the lines
and , and the curve . Set up integrals to find the volumes of the solids obtained by revolving this region about (i) the
-axis, and (ii) the -axis. (No need to evaluate the integrals in this problem.)
03
Shells volume - shells v. washers
Consider the region in the
-plane, in the first quadrant, bounded by the -axis on the left, by on the top, and on the bottom.
A 3D solid is given by revolving this region around the
-axis. (a) Find the volume of the solid using the method of shells.
(b) Attempt to find the volume of the solid using the method of washers/disks. Why is this harder? (TWO reasons!)
