Fubini's Theorem

Theorem Applied to Rectangular Domain

Let $f$ be integrable function with rectangular domain $R=[a,b]\times [c,d]$. Then, ${\int }_a^b{\int }_c^{d}f(x,y)dydx={\int }_c^d{\int }_a^{b}f(x,y)dxdy=\int {\int }_{R}f(x)dA$

General Theorem