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Math Help - Triple Integration. Coordinates of Centroid.

  1. #1
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    Triple Integration. Coordinates of Centroid.

    Hey guys. I can't seem to figure out this question. Here she is.

    Find the coordinates (x, y, z) of the centroid of the region which lies below the surface z^2 = 9xy

    and above the triangular region in the xy-plane enclosed by the straight lines y=9x, y=0 and x=16
    Last edited by Gotovina7; April 2nd 2008 at 06:59 PM.
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  2. #2
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    I know how to do the integration part, except I am a little confused on the bounds.
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  3. #3
    Senior Member JaneBennet's Avatar
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    I think the volume is

    V\ =\ \int_0^{16}\int_0^{9x}\int_0^{3\sqrt{xy}}\,\mathrm  {d}z\,\mathrm{d}y\,\mathrm{d}x

    Hence \overline{x}=\frac{1}{V}\int_0^{16}\int_0^{9x}\int  _0^{3\sqrt{xy}}{x}\,\mathrm{d}z\,\mathrm{d}y\,\mat  hrm{d}x, etc.
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  4. #4
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    Hmm thats what I thought, I guess ill give it a go again. Thanks. EDIT: Figured it out
    Last edited by Gotovina7; April 3rd 2008 at 08:23 AM.
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