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