Math 151 Spring 2008
Problem Set # 7: Volumes, Length and Surface Area
Starred Problems are due on Friday, March 7
Volumes by Slices or Cylindrical Shells
In problems 14, use
the method of disks
to determine the
volume
of the solid that is obtained
by revolving the region between the graph of
z
=
f
(
x
)
and the given interval about
the
x
axis.
1*.
f
(
x
) =
e
−
x
; [
−
ln (2)
,
ln (2)]
2.
f
(
x
) = sin
³
x
4
´
; [2
π,
3
π
]
3.
f
(
x
) =
r
x
x
2
+ 4
;
h
p
e
2
−
4
,
p
e
3
−
4
i
4*.
f
(
x
) =
r
1
x
2
+ 1
,
[
−
1
,
1]
.
In problems 5 and 6, use
the method of washers
to determine the
volume
of the solid that is
obtained by revolving the region between the graphs of
z
=
f
(
x
)
,
z
=
g
(
x
)
,
x
=
a
and
x
=
b
about
the
x
axis.
5.
f
(
x
) =
1
x
, g
(
x
) =
1
x
2
, x
= 1
, x
= 2
.
6*.
f
(
x
) = sin (
x
)
, g
(
x
) = cos (
x
)
, x
=
π/
4
, x
=
π/
2
In problems 710, use
the method of cylindrical shells
to determine the
volume
of the solid
that is obtained by revolving the graph of
z
=
f
(
x
)
on the given interval about
the
z
axis.
7.
f
(
x
) = sin
¡
x
2
¢
,
∙
r
π
6
,
r
π
4
¸
8*.
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 Winter '08
 Geveci
 Math

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