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

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

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

y

g(t)

t

(^0321)

• 1

1

Figure 13.5-1

2. The function fis continuous on [1, 5] and f >0, and selected values off are given
   below.

x 1 2 3 4 5

f(x) 2 4 6 8 10

Using 2 midpoint rectangles, approximate the area under the curve offforx=1to

x=5.

Answer:Midpoints arex=2 andx=4, and the width of each rectangle

=

5 − 1

2

=2.

Area≈ Area of Rect 1 + Area of Rect 2 ≈4(2)+8(2)≈24.

3. Set up an integral to find the area of the regions bounded by the graphs ofy=x^3 and
   y=x. Do not evaluate the integral.
   Answer:Graphs intersect atx=−1 andx=1. (See Figure 13.5-2.)

Area =

∫ 0

− 1

(

x^3 −x

)

dx+

∫ 1

0

(

x−x^3

)

dx.

Or, using symmetry, Area= 2

∫ 1

0

(

x−x^3

)

dx.

(–1, –1)

0

(1, 1)

y = x

x

y

y = x^3

Figure 13.5-2