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Math Help - First Moment using double integrals.

  1. #1
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    Question First Moment using double integrals.

    A thin plate with constant mass per unit area \rho has edges defind by the curves,

    x = \sqrt{a^{2}-y^{2}}, y=x, y=0,

    where a>0 is a constant. Find the first moment of the plate about the x-axis.

    See figure attached for my attempt. I've draw a quick sketch in the top right of the page.

    I'm first calculating the total mass of the plate, then I can find the first moment of the entire plate about the x-axis.

    i.e. M\bar{y} = \int \int_{R}y \rho dA

    I'm going to first solve M.

    Is there integral I've set up correct?

    The one step I'm worried about is when I was left to integrate,

    \sqrt{a^{2}-y^{2}}

    if I had done that one correctly.

    Is there perhaps another route of integrations that I should proceed with? Can anyone spot any other errors?

    Thanks again!
    Attached Thumbnails Attached Thumbnails First Moment using double integrals.-fmq.jpg  
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  2. #2
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    Bump, still looking for a little help on this one.
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