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Thread: Centroid problem

  1. #1
    Junior Member
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    Centroid problem

    Find the centroid of the area bounded by the curve
    $\displaystyle
    2y^2+2y-x-2=0
    $
    and the line $\displaystyle x=2y$.

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  2. #2
    Super Member wingless's Avatar
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    Do you know how to double integrate?

    $\displaystyle x=2y^2+2x-2$
    $\displaystyle x=2y$

    $\displaystyle \int \int ~dA$

    Using $\displaystyle dA = dx~dy$ will be better. It'll be easier to apply the bounds for y, because the functions are y's functions.

    A = $\displaystyle \int \int ~dx~dy$

    M_x = $\displaystyle \int \int y ~dx~dy$

    M_y = $\displaystyle \int \int x ~dx~dy$


    $\displaystyle \bar {x} = \frac{M_y}{A}$

    $\displaystyle \bar {y} = \frac{M_x}{A}$

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

    Now apply the bounds and integrate and so on..
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  3. #3
    Super Member wingless's Avatar
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    Here's another graph I made


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