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Math Help - "Washer" problem

  1. #1
    Newbie
    Joined
    Dec 2007
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    "Washer" problem

    Hi guys,

    Was wondering if anyone can help with the following problem:

    Find the volume of the solid genreated by revolving each region about the given axis.

    Question: The region in the second quadrant bounded above the curve y = -x^3, below by the x-axis, and on the left by the line x = -1, about the line x = -2

    Thank you
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  2. #2
    Super Member

    Joined
    May 2006
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    Lexington, MA (USA)
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    Hello, nmq3b!

    Find the volume of the solid formed by revolving fhe region in quadrant 2,
    bounded above the curve y \,=\,-x^3, below by the x-axis,
    and on the left by the line x = -1, about the line x = -2
    Code:
      :        *          |
      :                   |
      :         *         |
      :         |*        |
      :         |::*      |
      :         |:::::*.  |
    - + - - - - + - - - - * - - - - - -
     -2        -1         |   *
      :                   |      *
      :                   |       *
                          |

    "Shells" formula: . V \;=\;2\pi\int^b_a\text{(radius)(height)}\,dx

    We have: . \text{radius} = x + 2,\;\text{height} = -x^3

    Hence: . V \;=\;2\pi\int^0_{\text{-}1}(x+2)(-x^3)\,dx \;=\;-2\pi\int^0_{\text{-}1}(x^4 + 2x^3)\,dx

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