5.3 Volumes of Revolution: Shell Method

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