1. 7.2
Volume:
The Disc Method
The area under a curve
is the summation of an
infinite number of
rectangles.
If we take this rectangle
and revolve it about a
line, we have a disc.

2. This disc is nothing more
than a cylinder on it’s
side. r
The volume of a cylinder
is:
Disc
If we sum up an infinite number
of cylinders, we have the new
integration formula:
r = h & w = dx
This equation is for
a horizontal axis of
revolution.

3. Vertical axis of revolution

4. Ex. y = x2, y = 0, and x = 2 about the x-axis
r = y

5. Ex. y = x2, x = 0, and y = 4 about the y-axis
r = x

6. Find the radius for y = x2, y = 0, and x = 2
about the line x = 2
about the line x = 3 4 4 2 x
r = 2 - x
x = 3