90 Part I: The Questions
673. The region is bounded by the curves y = sin x,
y = cos x, x = 0, and x = π
2
and is rotated
about the x-axis.
674. The region is bounded by the curves
y
x
1
1
2
, y = 0, x = 0, and x = 1 and is
rotated about the x-axis.
675. The region is bounded by the curves
y = 3 + 2x – x
2
and x + y = 3 and is rotated
about the x-axis.
676. The region is bounded by the curves y = x
2
and x = y
2
and is rotated about the y-axis.
677. The region is bounded by the curves y = x
2/3
,
y = 1, and x = 0 and is rotated about the line
y = 2.
678. The region is bounded by the curves y = x
2/3
,
y = 1, and x = 0 and is rotated about the line
x = –1.
667. The region is bounded by the curves
x + 4y = 4, x = 0, and y = 0 and is rotated
about the x-axis.
668. The region is bounded by the curves
x = y
2
– y
3
and x = 0 and is rotated about
the y-axis.
669. The region is bounded by the curves
y
x
=
−1, y = 0, and x = 5 and is rotated
about the x-axis.
670. The region is bounded by the curves
y
x
= −
4 4
2 and y = 2 and is rotated about
the x-axis.
671. The region is bounded by the curves
x = y
2/3
, x = 0, and y = 8 and is rotated
about the y-axis.
672. The region is bounded by the curves
y
r
x
=
−
2
2
and y = 0 and is rotated about
the x-axis.