5 Steps to a 5 AP Calculus BC 2019

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