设区域
$$
D=\left\{(x, y) \mid x^2+y^2 \leq 1, y \geq 0\right\}
$$
连续函数 $f(x, y)$ 满足
$$
f(x, y)=y \sqrt{1-x^2}+x \iint_D f(x, y) \mathrm{d} x \mathrm{~d} y
$$
计算 $\iint_D x f(x, y) \mathrm{d} x \mathrm{~d} y$.
$\text{A.}$
$\text{B.}$
$\text{C.}$
$\text{D.}$