设 $\Sigma$ 为球面 $x^2+y^2+z^2=R^2$ 的下半球面的下侧, 将曲面 积分 $\iint_{\Sigma} x^2 y^2 z \mathrm{~d} x \mathrm{~d} y$ 化为二重积分为
A. $-\iint_{D_{x y}} x^2 y^2\left(-\sqrt{R^2-x^2-y^2}\right) \mathrm{d} x \mathrm{~d} y, \quad D_{x y}: x^2+y^2 \leq R^2$
B. $-\iint_{D_{x y}} x^2 y^2 \sqrt{R^2-x^2-y^2} \mathrm{~d} x \mathrm{~d} y$, $D_{x y}: x^2+y^2 \leq R^2$
C. $\iint_{D_{x y}} x^2 y^2\left(R^2-x^2-y^2\right) \mathrm{d} x \mathrm{~d} y$, $D_{x y}: x^2+y^2 \leq R^2$
D. $-\iint_{D_{x y}} x^2 y^2\left(R^2-x^2-y^2\right) \mathrm{d} x \mathrm{~d} y$, $D_{x y}: x^2+y^2 \leq R^2$