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Find the volume of revolution obtained by revolving around the y-axis the regio…

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Wize University Calculus 1 Textbook > Applications of Integration

Volumes of Revolution by Cylindrical Shells

3 Activities

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=3x2−x3y = 3x^2 -x^3. Use the method of cylindrical shells.
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+y2x=1+y^2, x=0x=0, y=1y=1, and y=2y=2 about the xx-axis.
Write the integrals representing the volume of the solid that is produced by revolving the region bounded between y=tan⁡3xy=\tan^3x, y=1y=1, and x=0x=0 about the line y=2y=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)4y=(x-1)^4 and 8x−y=88x-y=8 about the line x=10x=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+y2x=1+y^2, x=0x=0, y=1y=1, and y=2y=2 about the xx-axis.
Volumes of Revolution by Cylindrical Shells
Find the volume of the solid that is produced by revolving the region bounded between x=1+y2x=1+y^2, x=0x=0, y=1y=1, and y=2y=2 about the xx-axis.
Write the integrals representing the volume of the solid that is produced by revolving the region bounded between y=tan⁡3xy=\tan^3x, y=1y=1, and x=0x=0 about the line y=2y=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)4y=(x-1)^4 and 8x−y=88x-y=8 about the line x=10x=10. Do not compute the integral.
Find the volume of revolution obtained by revolving around the yy -axis the region of the fi rst quadrant bounded by the x-axis and the curve y=3x2−x3y = 3x^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)4y=(x-1)^4 and 8x−y=88x-y=8 about the line x=10x=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⁡3xy=\tan^3x, y=1y=1, and x=0x=0 about the line y=2y=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=exy=e^x and y=(e−1)x+1y=(e-1)x+1 about the line y=−1y=-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)4y=(x-1)^4 and 8x−y=88x-y=8 about the line x=10x=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⁡3xy=\tan^3x, y=1y=1, and x=0x=0 about the line y=2y=2 using both the washer method and the method of cylindrical shells. Do not compute the integrals.
Volumes of Revolution by Cylindrical Shells
Find the volume of the solid that is produced by revolving the region bounded between x=1+y2x=1+y^2, x=0x=0, y=1y=1, and y=2y=2 about the xx-axis.
Find the volume of the solid that is produced by revolving the region bounded between y=x2/4y=x^2/4, y=0y=0, and x=2x=2 about the yy-axis. Use the method of cylindrical shells.