5 Steps to a 5 AP Calculus BC 2019

268 STEP 4. Review the Knowledge You Need to Score High

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 12.3-2.

d

y

0 x

c

g(y)

Figure 12.3-2

Example 1

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

Step 1. Sketch the graph of f(x). See Figure 12.3-3.

0 1

–1

2

y

x

f(x)

Figure 12.3-3

Step 2. Set up integrals.

Area=

∣∣

∣∣

∫ 1

0

f(x)dx

∣∣

∣∣+

∫ 2

1

f(x)dx.