## Calculus (3rd Edition)

$\int_{0}^{4} \int_{x}^{4} f(x,y) \ dy \ dx = \int_{0}^{4} \int_{0}^{y} f(x,y) \ dx \ dy$
We are given the domain $0 \leq x \leq 4$ and $x \leq y \leq 4$. The iterated integral can be written for the domain $0 \leq y \leq 4$ and $0 \leq x \leq y$ as: $\iint_{D} f(x,y) d A= \int_{0}^{4} \int_{x}^{4} f(x,y) \ dy \ dx = \int_{0}^{4} \int_{0}^{y} f(x,y) \ dx \ dy$