Evaluate $\iiint_E xyz \; \mathrm dV $ Evaluate the triple integral:
$$\iiint_E xyz \; \mathrm dV$$
where $E$ is the solid: $0\le z\le 2,  0\le y\le z,  0\le x\le y$.
Please explain this, I'm so confused.

If you think of $dx$ as a change in distance, then $dydx$ would be (a change in distance) * (a change in distance) = (a little change in distance)^2 = (a little change in area). One more and it's a change in volume.
$dV$ = change in volume = $dxdydz$
$\int\int\int_{E}(xyz)dxdydz$
E = the volume in question, but you already have the bounds. Note that for this integral you need to integrate in a specific order. $x$ is evaluated from $0$ to $y$, so it should be evaluated before $y$ is. Otherwise you'll be left with a $y$ in your final answer. If we follow this pattern, we can see that $x$ must be integrated before $z$. That leaves $z$ to be integrated between two numbers, ultimately leaving you with the answer you want (ie a number).
$\int_{0}^{2}\int_{0}^{z}\int_{0}^{y}(xyz)dxdydz$
Hope that helps.
