Fubini's Theorem for Rectangular Prisms

Theorem

For $R=[a,b]\times [c,d]\times [p,q]$ we have:

$$\int \int {\int }_{R}fdV={\int }_a^b{\int }_c^d{\int }_p^{q}fdxdydz={\int }_q^p{\int }_a^b{\int }_c^{d}fdydxdz=\dots$$

For all order of integrations

Intuition

All orders of integrations will agree