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How can I find the coordinate $\bar{x}$ of centre of mass of the solid with the bounds $z=1-x^{2}$, $x=0$, $y=0$, $y=2$ and $z=0?$. Assuming a constant density.

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HINT...The volume has a constant cross section in the direction of the $y$ axis so you only need to find the centroid of the lamina formed by $z=1-x^2$ from $x=0$ to $x=1$

So you need to work out $$\bar{x}=\frac{\int_0^1x(1-x^2)dx}{\int_0^1(1-x^2)dx}$$

I hope this helps

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  • $\begingroup$ Glad to be of help. If this was what you were looking for, you can accept the answer so the question is closed.:) $\endgroup$ – David Quinn Apr 25 '17 at 5:22

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