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Math Help - Volume of a solid of revolution bounded by

  1. #1
    Junior Member bijosn's Avatar
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    Volume of a solid of revolution bounded by

    Determine the volum of a solid of revolution when the region bounded by y = \sqrt{x} and the straight lines y = 2 and x = 0 are rotated around the line x = 4

    my answer(which is wrong)
    V = 2\pi \int_{0}^{4} x ( 2 - \sqrt{x}) dx
    V = 2\pi  ( x^2 - \frac{2x^\frac{5}{2}}{5} )\big|_0^4

    = \frac{32\pi}{5}
    ??
    what am I doing wrong?
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  2. #2
    MHF Contributor Unknown008's Avatar
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    When you rotate about the x-axis (y = 0), you integrate with respect to x.

    When you rotate along the line x = 4, you integrate with respect to y.

    And can you tell why you picked x(2 - \sqrt{x})?
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  3. #3
    MHF Contributor
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    Hint: Translate your function and all the bounds left 4 units. The region does not change, but the calculations are easier because you can rotate around the x axis.
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