Answer
$\dfrac{9}{4}$
Work Step by Step
The domain $D$ for the given region can be expressed as: $1- \leq x \leq 2$ and $x^2 \leq y \leq x+2$
The iterated integral can be calculated as:
$\iint_{D} x d A=\int_{-1}^2 \int_{x^2}^{x+2} x dy dx\\=\int_{-1}^2 [xy]_{x^2}^{x+2} \ dx\\=\int_{-1}^2 x(x+2-x^2) dx \\=\dfrac{x^3}{3}+x^2-\dfrac{x^4}{4}|_{-1}^2\\=\dfrac{9}{4}$
