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

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

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

6. Find the area of the region bounded by the
   graphsy=

√

x,y=−x, andx=4.

7. Find the area of the region bounded by the
   curvesx=y^2 andx=4.


8. Find the area of the region bounded by the
   graphs of all four equations:
   f(x)=sin

(

x

2

)

;x-axis; and the lines,

x=

π

2

andx=π.

9. Find the volume of the solid obtained by
   revolving about thex-axis, the region
   bounded by the graphs ofy=x^2 +4, the
   x-axis, they-axis, and the linesx=3.


10. The area under the curvey=

1

x

fromx= 1

tox=kis 1. Find the value ofk.

11. Find the volume of the solid obtained by
    revolving about they-axis the region
    bounded byx=y^2 +1,x=0,y=−1, and
    y=1.


12. LetRbe the region enclosed by the graph
    y= 3 x, thex-axis, and the linex=4. The
    linex=adivides regionRinto two regions
    such that when the regions are revolved
    about thex-axis, the resulting solids have
    equal volume. Finda.

Part B Calculators are allowed.

13. Find the volume of the solid obtained by
    revolving about thex-axis the region
    bounded by the graphs off(x)=x^3 and
    g(x)=x^2.


14. The base of a solid is a region bounded by
    the circlex^2 +y^2 =4. The cross sections of
    the solid perpendicular to thex-axis are
    equilateral triangles. Find the volume of the
    solid.
    15. Find the volume of the solid obtained by
    revolving about they-axis, the region
    bounded by the curvesx=y^2 andy=x−2.
    For Problems 16 through 19, find the volume
    of the solid obtained by revolving the region as
    described below. (See Figure 13.6-2.)

R 1

C(0, 8)

A(2, 0)

R 2

y

x

B(2, 8)

y = x^3

0

Figure 13.6-2

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 of f(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.