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    Cylindrical Shells

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    The region bounded by the curve and the lines and is revolved around the x-axis to form a solid S.
    The volume of S by the method of washers is given by the integral .
    Find the volume using the method of cylindrical shells. Please show the complete solution (particularly how to find the cross-sectional area), including all work.

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    Solution Preview

    At a distance x from the origin, draw cylinder of radius r
    r =x^2 + 1
    and height dh = dx.
    hence the volume of ...

    Solution Summary

    This uses the cylindrical shell method to find volume.