Answer
$3e^{12}+e^8$
Work Step by Step
The domain $D$ for the given region can be expressed as: $4 \leq y \leq 8$ and $4\leq x\leq 12-x$
The iterated integral can be calculated as:
$\iint_{D} e^{x+y} d A=\int_4^8 \int_{4}^{12-x} e^{x+y} dx dy\\=\int_4^8 e^x (e^{12-x}-e^4) \ dx\\=\int_4^8 (e^{12}-e^{4+x}) \ dx \\=4e^{12} e^{12}+e^8\\=3e^{12}+e^8\approx 491245.3$
