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5.3 Volumes of Revolution: Shell Method

5.3 Volumes of Revolution: Shell Method. Remember, in the Disk Method we place the typical element perpendicular to the axis of rotation. Now, for the Shell Method , we place the typical element parallel to the axis of rotation. When we rotate it, it produces a cylindrical shell.

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5.3 Volumes of Revolution: Shell Method

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  1. 5.3 Volumes of Revolution: Shell Method Remember, in the Disk Method we place the typical element perpendicular to the axis of rotation. Now, for the Shell Method, we place the typical element parallel to the axis of rotation. When we rotate it, it produces a cylindrical shell. But, in both methods, if the width of the element is dx, then the variable of integration is x; if the width of the element is dy, then the variable of integration is y. Important: for the Disk Method, the elementary volume was For the Shell Method, the elementary volume is 1

  2. Exercise: Use the shell method to find the volume generated by revolving the region bounded by a. about the x-axis b. about the y-axis 2

  3. Homework: Section 5.3: 3,15,19,27,41. 3

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