Answer
$\frac{1}{8}$
Work Step by Step
We can define the domain D as follows:
$D=\{(x,y)|0\leq x\leq 1, 0\leq y\leq \sqrt{1-x^2}\}$
Therefore, $$\int\int_DxydA=\int_0^1\int_0^\sqrt{1-x^2}xydydx$$
$$=\int_0^1\frac{1}{2}xy^2|_{y=0}^{y=\sqrt{1-x^2}}dx$$
$$=\int_0^1\frac{1}{2}x(1-x^2)dx$$
$$=-\frac{1}{8}(1-x^2)^2|_0^1$$
$$=\frac{1}{8}$$
