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Thread: Finding the coordinates of a centroid

  1. #1
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    Finding the coordinates of a centroid

    Hi I made an attempt at this problem but Im not quite sure if I have the correct procedure.

    find the exact coordinates of the centroid.

    $\displaystyle y = 100 - x^2$
    $\displaystyle y = 0$

    So the graphs intersect at x=-10 and 10

    the centroid is $\displaystyle (\bar{x}, \bar{y})$

    and $\displaystyle \bar{x}= \frac{M}{m}$

    So $\displaystyle M = 2\int_0^{10} \! xf(x) \, dx.=$
    $\displaystyle 2\int_0^{10} \! x(100-x^2) \, dx.=$
    $\displaystyle 2[50x^2-\frac{1}{4}x^4]\bigg|_0^{10}=$
    $\displaystyle 5000$

    $\displaystyle m = 2\int_0^{10} \! f(x) \, dx.=$
    $\displaystyle 2\int_0^{10} \! (100-x^2)\, dx.=$
    $\displaystyle 2[100x-\frac{1}{3}x^3]\bigg|_0^{10}=$
    $\displaystyle \frac{4000}{3}$

    Therefore, $\displaystyle \frac{M}{m} = \frac{15}{4}$

    and by symmetry the centroid is (15/4, 15/4) right??
    Last edited by mmattson07; Oct 21st 2009 at 10:56 PM.
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  2. #2
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    tried using this formula and I arrive at the same answer

    $\displaystyle \bar{x} = \frac{1}{A}2\int_0^{10} \! x(100-x^2) \, dx.$

    Where $\displaystyle A = 2\int_0^{10} \! (100-x^2) \, dx.$

    I know its obvious why, but am I doing this problem correctly?
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