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

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

Areas and Volumes 281

Ifx=g(y) is continuous and non-negative on [c,d], then the area under the curve ofg
fromctodis:

Area

∫d

c

g(y)dy.(See Figure 13.3-2.)

d

y

x

0

c

g(y)

Figure 13.3-2

Example 1

Find the area under the curve off(x)=(x−1)^3 fromx=0tox=2.

Step 1: Sketch the graph off(x). (See Figure 13.3-3.)

0 1

• 1

2

y

x

f(x)

Figure 13.3-3

Step 2: Set up the integrals.

Area=

∣∣

∣∣

∫ 1

0

f(x)dx

∣∣

∣∣+

∫ 2

1

f(x)dx.