# Thread: Triple Integration. Coordinates of Centroid.

1. ## 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 $x=16$

2. I know how to do the integration part, except I am a little confused on the bounds.

3. 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.

4. Hmm thats what I thought, I guess ill give it a go again. Thanks. EDIT: Figured it out