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Math Help - Volume Generated by Rotating a Region

  1. #1
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    Volume Generated by Rotating a Region

    I am trying to find the volume generated by rotating the region bounded by y=4+x-x^2 and y=4-x about the y-axis

    I got an answer of 4\pi/3
    using this: \pi \int_0^2 (4+x-x^2)-(4-x)

    I feel as if this volume is to small but since is rotated about the y-axis I dont have any other values to add that I can think of to account for the area rotated not touching the y-axis.
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  2. #2
    Senior Member
    Joined
    Jan 2010
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    Since you are sweeping along the x-direction and rotating about the y-axis, you are using the "shell" method, which means your integral should be of the form:

    2\pi \int r(x) \, h(x) \, dx

    where r(x) is the radius and h(x) is the height, both in terms of x.

    You have correctly identified the height as (4+x-x^2)-(4-x) but you are missing the radius and the "2" in the front. Your limits of integration are correct, also.
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