89
Chapter 11: Applications of Integration
Finding Volumes Using Disks
and Washers
662–681 Find the volume of the solid obtained by
revolving the indicated region about the given line.
(Tip: Making a rough sketch of the region that’s
being rotated is often useful.)
662. The region is bounded by the curves y = x
4
,
x = 1, and y = 0 and is rotated about the
x-axis.
663. The region is bounded by the curves
x
y
= sin , x = 0, y = 0, and y = π and is
rotated about the y-axis.
664. The region is bounded by the curves y x
= 1 ,
x = 3, x = 5, and y = 0 and is rotated about
the x-axis.
665. The region is bounded by the curves
y
x
1 , x = 1, x = 3, and y = 0 and is rotated
about the x-axis.
666. The region is bounded by the curves
y = csc x, x = π
4
, x = π
2
, and y = 0 and is
rotated about the x-axis.
653. y = sin x, y = cos x, x = − π
4
, x = π
2
654. x = y
2
, x
y
=
, y = 0, y = 2
655. x = y
2
– y, x = 4y
656. y = x – 1, y
2
= 2x + 6
657. y = x, x + 2y = 0, 2x + y = 3
658. y x
=
+4, y x
= + 4
2
659. y
x
= 2 , y = x
2
– 3
660. y = cos x, y = sin 2x, x = 0, x = π
2
661. y = 2e
2x
, y = 3 – 5e
x
, x = 0