CHAPTER 22
22.8
Fig. 22-5
Fig. 22-6
22.9
The region below the quarter-circle x
2 + y
2 = r
2 (x>0, y >0) and above the line y = a, where 0 about the y-axis. (This gives the volume of a polar cap of a sphere.)
See Fig. 22-6. We use the disk formula along the y-axis:
22.10
The region bounded by y = 1 + x
2
and y = 5; about the x-axis. (See Fig. 22-7.)
Fig. 22-7
Fig. 22-4
22.6
The region of Problem 22.5, about the y-axis.
We use the cylindrical shell formula:
The region of Problem 21.39, about the jc-axis.
22.7
The curves intersect at (0, 0) and (1,1). The upper curve is
and the lower curve is
We use the circular ring formula:
The region inside the circle x
2 + y
2 = r
2 with 0 from a sphere of radius r by a pipe of radius a whose axis is a diameter of the sphere.)
We shall consider only the region above the *-axis (Fig. 22-5), and then, by symmetry, double the result. We
use the cylindrical shell formula:
We multiply by 2 to obtain the
answer
174