5 Steps to a 5 AP Calculus BC 2019

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

3. (See Figure 12.9-2.)
   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 12.9-2

4. (See Figure 12.9-3.)
   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

023451

y

x

f(x) =x^1

Not to Scale

Figure 12.9-3

5. (See Figure 12.9-4.)

Trapezoid Rule =

b−a

2 n

(

f(a)+ 2 f(x 1 )

+ 2 f(x 2 )+f(b)

)

.

A=

3 − 0

2(3)

(f(0)+ 2 f(1)+ 2 f(2)+ f(3))

=

1

2

(1+ 4 + 10 +10)=

25

2

y

x

y = x^2 + 1

Not to

Scale

0123

Figure 12.9-4