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Math Help - Centroid

  1. #1
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    Centroid

    Find the centroid of the region bounded by
    y=3x^2+6x, y=0 and x=3.

    So what I've done so far
    0<x<3
    0<y<3x^2+6x
    those are the bounds
    and i take the double integral using those bound to find m
    but I don't know what function to use I originally used 3x^2+6x but thats not correct.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by koalamath View Post
    Find the centroid of the region bounded by
    y=3x^2+6x, y=0 and x=3.

    So what I've done so far
    0<x<3
    0<y<3x^2+6x
    those are the bounds
    and i take the double integral using those bound to find m
    but I don't know what function to use I originally used 3x^2+6x but thats not correct.
    I don't have the time right now to answer, but a centroid problem [where I have worked out double integrals] was asked here...

    --Chris
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  3. #3
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    my problem isn't the actual process of integration, I don't know what to integrate
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by koalamath View Post
    my problem isn't the actual process of integration, I don't know what to integrate
    Your two integrals would be

    \bar{x}=\frac{1}{\int_0^3\left(3x^2+6x\right)\,dx}  \int_0^3\int_0^{3x^2+6x}x\,dy\,dx and

    \bar{y}=\frac{1}{\int_0^3\left(3x^2+6x\right)\,dx}  \int_0^3\int_0^{3x^2+6x}y\,dy\,dx

    where \int_0^3\left(3x^2+6x\right)\,dx is the area of the region R

    Do you see how I got these? It's pretty much "plug and chug" into the formula for \bar{x} and \bar{y}.

    --Chris
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  5. #5
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    no i don't
    the formula for m is the double integral of p(x,y) where p is the density function.

    Your m doesn't make sense to me how did you find 3x^2+6x to be the density function and why isn't a double integral ?
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  6. #6
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by koalamath View Post
    no i don't
    the formula for m is the double integral of p(x,y) where p is the density function.

    Your m doesn't make sense to me how did you find 3x^2+6x to be the density function and why isn't a double integral ?
    Are you trying to find the center of mass or the centroid?

    They are two different definitions...

    Center of mass requires a density function, whereas a centroid doesn't.

    --Chris
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  7. #7
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    aren't they the same thing?
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