Answer
$\dfrac{e^{16}-1}{4} $
Work Step by Step
The domain $D$ for given region can be expressed as: $0 \leq x \leq 4$ and $\dfrac{x}{4} \leq y \leq \dfrac{3x}{4}$
The iterated integral can be calculated as:
$\iint_{D} f(x,y) d A=\int_0^4 \int_{x/4}^{3x/4} e^{x^2} dy dx\\=\int_0^4 (ye^{x^2})_{x/4}^{3x/4} dx \\=\int_0^4 [\dfrac{3x}{4}e^{x^2}-\dfrac{x}{4}e^{x^2}] \ dx \\=\dfrac{1}{4}[e^{x^2}]_0^4\\=\dfrac{e^{16}-1}{4} $
