(Solved): The shaded area shown in \( \quad \) is bounded by the line \( y=x \mathrm{~m} \) and the curve \( ...

The shaded area shown in \( \quad \) is bounded by the line \( y=x \mathrm{~m} \) and the curve \( y^{2}=1.5 x \mathrm{~m}^{2} \), where \( x \) is in \( \mathrm{m} \). Suppose that \( a=1.5 \mathrm{~m} \). Determine the moment of inertia for the shaded area about the \( y \) axis. Express your answer to three significant figures and include the appropriate units.