5 Steps to a 5 AP Calculus BC 2019

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

For Problems 16 through 19, find the

volume of the solid obtained by revolving

the region as described below.

(See Figure 12.7-2.)

R 1

C(0,8)

A(2,0)

R 2

y

x

B(2,8)

y = x^3

0

Figure 12.7-2

16. R 1 about thex-axis.


17. R 2 about they-axis.


18. R 1 about the line

←→

BC.

19. R 2 about the line

←→

AB.

20. The functionf(x) is continuous on [0, 12]
    and the selected values off(x) are shown in
    the table.

x 0 2 4 6 8 10 12

f(x) 1 2.24 3 3.61 4.12 4.58 5

Find the approximate area under the curve

off from 0 to 12 using three midpoint

rectangles.

21. Find the area bounded by the curve defined
    byx=2 costandy=3 sintfromt=0to
    t=π.


22. Find the length of the arc ofr=sin^2

(

θ

2

)

fromθ=0toθ=π.

23. Find the area of the surface formed when
    the curve defined byx=etsintand
    y=etcostfromt=0tot=
    π
    2

is revolved

about thex-axis.

24. Find the area bounded byr= 2 +2 sinθ.


25. The acceleration vector for an object is
    〈−et, et〉. Find the position of the object at
    t=1 if the initial velocity isv 0 =

〈

3, 1

〉

and

the initial position of the object is at the

origin.

12.8 Cumulative Review Problems

(Calculator) indicates that calculators are
permitted.

26. If

∫a

−a

ex

1

dx=k, find

∫a

0

ex

2

dxin terms

ofk.

27. A man wishes to pull a log over a 9 foot
    high garden wall as shown in
    Figure 12.8-1. He is pulling at a rate of
    2 ft/sec. At what rate is the angle between
    the rope and the ground changing when
    there are 15 feet of rope between the top of
    the wall and the log?

θ

9 ft

wall

rope

rope

log

Figure 12.8-1

28. (Calculator) Find a point on the parabola
    y=

1

2

x^2 that is closest to the point (4, 1).