5 Steps to a 5 AP Calculus AB 2019 - William Ma

MA 3972-MA-Book April 11, 2018 16:1

Areas and Volumes 293

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 13.4-5.)

0

0

a b

f(x)

g(y)

y

x

x

y

d

c

Figure 13.4-5

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 13.4-6.)