Answer
$ \dfrac{e-2}{2}$
Work Step by Step
The domain $D$ for given region can be expressed as: $0 \leq x \leq 1$ and $1\leq y\leq e^{x^2}$
The iterated integral can be calculated as:
$\iint_{D} f(x,y) d A= \int_{0}^{1} \int_{1}^{e^{x^2}} x \ dy \ dx \\= \int_{0}^{1} [xy]_1^{e^{x^2}} \ dx\\= \int_{0}^{1} [xe^{x^2}-x) \ dx \\=[\dfrac{e^{x^2}}{2}-\dfrac{x^2}{2}]_0^1 \\= \dfrac{e-2}{2}$
