Finding the center of mass

Question

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.

Answer 1

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