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Center of mass

  1. Feb 12, 2013 #1
    1. The problem statement, all variables and given/known data
    constant density. region bounded by y=x-x^2, y=-x.


    2. Relevant equations
    this is according to the formula my instructor gave me:

    Y(bar) - (1/2)(integral)(a to b)(δ)(f(x) ^2 - g(x)^2) dx
    -----------------------------------------------
    (integral)(a to b) (δ) (f(x) - g(x)) dx

    3. The attempt at a solution

    Y(bar) = (1/2) (integral)(0 to 2) [ δ ((x-x^2)^2 - (-x)^2) dx ]
    ----------------------------------------------------
    (integral)(0 to 2) [δ ((x-x^2) - (-x)) dx]

    (1/2)(integral) (0 to 2) [δ (-2x^2 + x^4) dx ] = 8δ/15
    (integral)(0 to 2) [δ ((x-x^2) - (-x)) dx] = 4δ/3

    Y(bar) = 2/5 ; however, the answer is -3/5.
     
  2. jcsd
  3. Feb 12, 2013 #2
    sorry. solved.
     
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