长方体上的三重积分

One more layer of sums

A worked evaluation on the unit cube

Six orders, one value

What the number means

What is the value of $\iiint_{[0,1]^3} x y z\, dV$ over the unit box?

Which integrand over the box $[0, 2] \times [0, 1] \times [0, 1]$ lets the triple integral split into a product of one-variable integrals?

The integral of a temperature field over the unit cube is $3$, and the cube's volume is $1$. What is the average temperature?

Compute the inner pass $\int_0^1 x y z\, dz$ with $x$ and $y$ frozen, giving the result like 3*x*y/2.

Give $\iiint_B 1\, dV$ over the box $[0, 2] \times [0, 1] \times [0, 3]$, as a plain number.