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.