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

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

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

2. (See Figure 13.8-1.)

y

x

x = – 1 x = 2

y = x^3

– (^120)
Figure 13.8-1

A=

∣∣

∣

∣

∫ 0

− 1

x^3 dx

∣∣

∣

∣+

∫ 2

0

x^3 dx

=

∣∣

∣∣

∣

[

x^4

4

] 0

− 1

∣∣

∣∣

∣

+

[

x^4

4

] 2

0

=

∣∣

∣∣

∣^0 −

(− 1 )^4

4

∣∣

∣∣

∣+

(

24

4

− 0

)

=

1

4

+ 4 =

17

4

3. (See Figure 13.8-2.)
   Set 2x− 6 =0;x=3 and

f(x)=

{

2 x−6ifx≥ 3

−(2x−6) ifx< 3.

A=

∫ 3

0

−(2x−6)dx+

∫ 4

3

(2x−6)dx

=

[

−x^2 + 6 x

] 3

0 +

[

x^2 − 6 x

] 4

3

=

[

−(3)^2 +6(3)

]

− 0 +

[

42 +6(4)

]

−

[

32 −6(3)

]

= 9 + 1 = 10

043

y

x

y = 2x – 6

x = 0 x = 4

Figure 13.8-2

4. (See Figure 13.8-3.)
   Length ofΔx 1 =

5 − 1

4

=1.

Area of RectI= f(2)Δx 1 =

1

2

(1)=

1

2

.

Area of RectII= f(3)Δx 2 =

1

3

(1)=

1

3

.

Area of RectIII= f(4)Δx 3 =

1

4

(1)=

1

4

.

Area of RectIV= f(5)Δx 4 =

1

5

(1)=

1

5

.

Total Area=

1

2

+

1

3

+

1

4

+

1

5

=

77

60

.

I II

III IV

02341 5

y

x

f(x) =^1 x

Not to scale

Figure 13.8-3