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Volumes of Revolution by Cylindrical Shells
Related Topics
Wize University Calculus 1 Textbook > Applications of Integration
Volumes of Revolution by Cylindrical Shells
3 Activities
Find the volume of the solid that is produced by revolving the region bounded between
x
=
1
+
y
2
x=1+y^2
x
=
1
+
y
2
,
x
=
0
x=0
x
=
0
,
y
=
1
y=1
y
=
1
, and
y
=
2
y=2
y
=
2
about the
x
x
x
-axis.
Answer
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More Volumes of Revolution by Cylindrical Shells Questions:
Volumes of Revolution by Cylindrical Shells
Find the volume of the solid that is produced by revolving the region bounded between
x
=
1
+
y
2
x=1+y^2
x
=
1
+
y
2
,
x
=
0
x=0
x
=
0
,
y
=
1
y=1
y
=
1
, and
y
=
2
y=2
y
=
2
about the
x
x
x
-axis.
Write the integrals representing the volume of the solid that is produced by revolving the region bounded between
y
=
tan
3
x
y=\tan^3x
y
=
tan
3
x
,
y
=
1
y=1
y
=
1
, and
x
=
0
x=0
x
=
0
about the line
y
=
2
y=2
y
=
2
using both the washer method and the method of cylindrical shells. Do not compute the integrals.
Write an integral representing the volume of the solid that is produced by revolving the region bounded between
y
=
(
x
−
1
)
4
y=(x-1)^4
y
=
(
x
−
1
)
4
and
8
x
−
y
=
8
8x-y=8
8
x
−
y
=
8
about the line
x
=
10
x=10
x
=
10
. Do not compute the integral.
Volumes of Revolution by Cylindrical Shells
Find the volume of the solid that is produced by revolving the region bounded between
x
=
1
+
y
2
x=1+y^2
x
=
1
+
y
2
,
x
=
0
x=0
x
=
0
,
y
=
1
y=1
y
=
1
, and
y
=
2
y=2
y
=
2
about the
x
x
x
-axis.
Volumes of Revolution by Cylindrical Shells
Find the volume of the solid that is produced by revolving the region bounded between
x
=
1
+
y
2
x=1+y^2
x
=
1
+
y
2
,
x
=
0
x=0
x
=
0
,
y
=
1
y=1
y
=
1
, and
y
=
2
y=2
y
=
2
about the
x
x
x
-axis.
Write the integrals representing the volume of the solid that is produced by revolving the region bounded between
y
=
tan
3
x
y=\tan^3x
y
=
tan
3
x
,
y
=
1
y=1
y
=
1
, and
x
=
0
x=0
x
=
0
about the line
y
=
2
y=2
y
=
2
using both the washer method and the method of cylindrical shells. Do not compute the integrals.
Write an integral representing the volume of the solid that is produced by revolving the region bounded between
y
=
(
x
−
1
)
4
y=(x-1)^4
y
=
(
x
−
1
)
4
and
8
x
−
y
=
8
8x-y=8
8
x
−
y
=
8
about the line
x
=
10
x=10
x
=
10
. Do not compute the integral.
Find the volume of revolution obtained by revolving around the
y
y
y
-axis the region of the fi rst quadrant bounded by the x-axis and the curve
y
=
3
x
2
−
x
3
y = 3x^2 -x^3
y
=
3
x
2
−
x
3
. Use the method of cylindrical shells.
Using the method of shells, write an integral representing the volume of the solid that is produced by revolving the region bounded between
y
=
(
x
−
1
)
4
y=(x-1)^4
y
=
(
x
−
1
)
4
and
8
x
−
y
=
8
8x-y=8
8
x
−
y
=
8
about the line
x
=
10
x=10
x
=
10
. Do not compute the integral.
Write the integrals representing the volume of the solid that is produced by revolving the region bounded between
y
=
tan
3
x
y=\tan^3x
y
=
tan
3
x
,
y
=
1
y=1
y
=
1
, and
x
=
0
x=0
x
=
0
about the line
y
=
2
y=2
y
=
2
using both the washer method and the method of cylindrical shells. Do not compute the integrals.
Write the integrals representing the volume of the solid that is produced by revolving the region bounded between
y
=
e
x
y=e^x
y
=
e
x
and
y
=
(
e
−
1
)
x
+
1
y=(e-1)x+1
y
=
(
e
−
1
)
x
+
1
about the line
y
=
−
1
y=-1
y
=
−
1
using both the washer method and the method of cylindrical shells. Do not compute the integrals.
Write an integral representing the volume of the solid that is produced by revolving the region bounded between
y
=
(
x
−
1
)
4
y=(x-1)^4
y
=
(
x
−
1
)
4
and
8
x
−
y
=
8
8x-y=8
8
x
−
y
=
8
about the line
x
=
10
x=10
x
=
10
. Do not compute the integral.
Write the integrals representing the volume of the solid that is produced by revolving the region bounded between
y
=
tan
3
x
y=\tan^3x
y
=
tan
3
x
,
y
=
1
y=1
y
=
1
, and
x
=
0
x=0
x
=
0
about the line
y
=
2
y=2
y
=
2
using both the washer method and the method of cylindrical shells. Do not compute the integrals.
Find the volume of revolution obtained by revolving around the
y
-axis the region of the fi rst quadrant bounded by the
x
-axis and the curve
y
=
3
x
2
−
x
3
y = 3x^2 -x^3
y
=
3
x
2
−
x
3
. Use the method of cylindrical shells.
Find the volume of the solid that is produced by revolving the region bounded between
y
=
x
2
/
4
y=x^2/4
y
=
x
2
/4
,
y
=
0
y=0
y
=
0
, and
x
=
2
x=2
x
=
2
about the
y
y
y
-axis. Use the method of cylindrical shells.