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Calculus I (Practice Problems) / Applications of Integrals / Volumes of Solids of Revolution/Method of Cylinder   [Notes] [Practice Problems] [Assignment Problems]

Calculus I - Practice Problems
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For problems 1  8 use the method of cylinders to determine the volume of the solid obtained by rotating the region bounded by the given curves about the given axis.

 

1. Rotate the region bounded by , the x-axis and the y-axis about the x-axis. [Solution]

 

2. Rotate the region bounded by , ,  and the x-axis about the y-axis. [Solution]

 

3. Rotate the region bounded by  and  about the y-axis.  For this problem assume that . [Solution]

 

4. Rotate the region bounded by  and  about the x-axis.  For this problem assume that . [Solution]

 

5. Rotate the region bounded by ,  and  about the line . [Solution]

 

6. Rotate the region bounded by  and  about the line . [Solution]

 

7. Rotate the region bounded by  and  about the line . [Solution]

 

8. Rotate the region bounded by , ,  and  about the line . [Solution]

 

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Volumes of Solids of Revolution / Method of Rings Previous Section   Next Section More Volume Problems
Integrals Previous Chapter   Next Chapter Extras

Calculus I (Practice Problems) / Applications of Integrals / Volumes of Solids of Revolution/Method of Cylinder    [Notes] [Practice Problems] [Assignment Problems]

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