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

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

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

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 13.3-11.)

[–π, π] by [–1.5, 1.5]

Figure 13.3-11

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 that you can 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 13.3-12.)

0

• 5

e e^3

y x = e x = e^3

x

xy = 1

y = – 5

Figure 13.3-12