Multiple Integral Splitting Theorem

Theorem (2 Variable)

$${\int }_a^b{\int }_c^{d}f(x)g(x)dxdy=[{\int }_c^{d}f(x)dx][{\int }_a^{b}g(x)dy]$$

Theorem (3 Variable)

$${\int }_a^b{\int }_c^d{\int }_e^{f}f(x)g(x)h(x)dxdydz=[{\int }_e^{f}f(x)dx][{\int }_c^{d}g(x)dy][{\int }_a^{b}h(x)dz]$$