# 16.2 | Iterated Integrals

Fubini’s Theorem: If $$f$$ is continuous on the rectangle $$R = \lbrace (x,y) \; | \; a \leq x \leq b, \; c \leq y \leq d \rbrace$$, then

$$\iint_R f(x,y) \; dA = \int_a^b \int_c^d f(x,y) \; dy \; dx = \int_c^d \int_a^b f(x,y) \; dx \; dy$$
\begin{aligned} \iint_R f(x,y) \; dA & = \int_a^b \int_c^d f(x,y) \; dy \; dx \\ & = \int_c^d \int_a^b f(x,y) \; dx \; dy \end{aligned}
\begin{aligned} \iint_R f(x,y) \; dA &= \int_a^b \int_c^d f(x,y) \; dy \; dx \\ & = \int_c^d \int_a^b f(x,y) \; dx \; dy \end{aligned}