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    Set Up Integral for Volume; Revolve Bounded Region

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    1. Draw a representative strip and set up an integral for the volume of the solid formed by revolving the given region:
    a) about the x-axis
    b) about the y-axis
    *Set up the integral only; DO NOT EVALUATE
    I. The region bounded by the curves {see attachment for curves and diagram}

    2. Find the volume by:
    a) disk/washer method
    b) shell method
    I. Revolve the region bounded by y = x[squared] and y = x [cubed] about the y-axis
    II. Revolve the region bounded by y = x, y = x2, and y = 1 about the y-axis

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    Solution Summary

    The revolve bounded regions for an integral is found. The volumes are given.