Answer
$40.5$
Work Step by Step
The domain $D$ for given region can be expressed as: $0 \leq y \leq 2$ and $y\leq x\leq 4$
The iterated integral can be calculated as:
$\iint_{D} x^2y d A=\int_0^2 \int_{y}^4 x^2y dx dy\\=\int_0^2 \dfrac{x^3y}{3}|_{y}^{4} dy \\=\int_0^2 \dfrac{y^3}{3}(64-y^3) \ dy \\=[\dfrac{32y^2}{3}-\dfrac{y^5}{15}]_0^2 \\=40.5$
