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

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

E 16.2 Exercises