Since you are rotating around the
axis, this will be a
integral.
The graphs intersect where the equations are equal...
or
.
When
, so they intersect at
.
The volume is calculated by rotating the area around the
axis.
This area needs to be thought of as a series of rectangles, which when rotated, become cylinders.
The length of each rectangle is
and the width is
, a small change in
.
When rotated, each cylinder has a radius the same as the length of each rectangle, so the circular cross-sectional area is
. The height of each cylinder is the same as the width of each rectangle,
.
Therefore the volume of each cylinder is
.
So the entire volume can be approximated by
, and when you increase the number of cylinders, this sum converges on an integral and the approximation becomes exact.
So
.