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Math Help - Centroid problem

  1. #1
    Junior Member
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    Centroid problem

    Find the centroid of the area bounded by the curve
    <br />
2y^2+2y-x-2=0<br />
    and the line x=2y.

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

    x=2y^2+2x-2
    x=2y

    \int \int ~dA

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

    A = \int \int ~dx~dy

    M_x = \int \int y ~dx~dy

    M_y = \int \int x ~dx~dy


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

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

    And the centroid is 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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