D由y^2=(9)/(2)x与直线x=2所围成，求均匀薄片(面密度设为rho)D绕x轴的转动惯量的数值为I_x=?() A (52)/(5)rho; B (62)/(5)rho; C (72)/(5)rho; D (82)/(5)rho;

区域 $D$ 由抛物线 $y^2 = \frac{9}{2}x$ 和直线 $x = 2$ 围成。将转动惯量公式转换为迭代积分： \[ I_x = \rho \int_0^2 \int_{-\frac{3}{\sqrt{2}}\sqrt{x}}^{\frac{3}{\sqrt{2}}\sqrt{x}} y^2 \, dy \, dx \] 计算内积分： \[ \int_{-\frac{3}{\sqrt{2}}\sqrt{x}}^{\frac{3}{\sqrt{2}}\sqrt{x}} y^2 \, dy = \frac{9}{\sqrt{2}} x^{3/2} \] 计算外积分： \[ \rho \int_0^2 \frac{9}{\sqrt{2}} x^{3/2} \, dx = \rho \cdot \frac{9}{\sqrt{2}} \cdot \frac{2}{5} \cdot 2^{5/2} = \frac{72}{5} \rho \] 答案：$\boxed{C}$。