280 STEP 4. Review the Knowledge You Need to Score High
The Disc Method
The volume of a solid of revolution using discs:
Revolving about thex-axis:
V=π
∫b
a
(f(x))^2 dx, where f(x)=radius.
Revolving about they-axis:
V=π
∫d
c
(g(y))^2 dy, whereg(y)=radius.
(See Figure 12.4-5.)
0
0
a b
f(x)
g(y)
y
x
x
y
d
c
Figure 12.4-5
Revolving about a liney=k:
V=π
∫b
a
(f(x)−k)^2 dx, where
∣∣
f(x)−k
∣∣
=radius.
Revolving about a linex=h:
V=π
∫d
c
(g(y)−h)^2 dy, where
∣∣
g(y)−h
∣∣
=radius.
(See Figure 12.4-6.)