Example 2.3.5: Volume of a rectangular box

The box occupies $0\le x\le a$, $0\le y\le b$, $0\le z\le d$. With $dV=dxdydz$ from Eq. (2.3.12),

which reduces to $a^3$ for a cube. Because the box has its faces on coordinate surfaces, all limits are constants and the order of integration is irrelevant.