Areas, Volumes, and Arc Lengths 275
Example 3
Using a calculator, find the area of the region bounded byy=sinxandy=
x
2
between
0 ≤x≤π.
Step 1. Sketch a graph. (See Figure 12.3-11.)
[−π,π] by [−1.5,1.5]
Figure 12.3-11
Step 2. Find the points of intersection.
Using the [Intersection] function of the calculator, the intersection points arex= 0
andx= 1 .89549.
Step 3. Enter nInt(sin(x)−. 5 x, x,0,1.89549) and obtain 0. 420798 ≈ 0 .421.
(Note: You could also use the
∫
function on your calculator and get the same
result.)
Example 4
Find the area of the region bounded by the curvexy=1 and the linesy=−5,x=e, and
x=e^3.
Step 1. Sketch a graph. (See Figure 12.3-12.)
0
–5
ee^3
y x = ex = e^3
x
xy = 1
y = –5
Figure 12.3-12