The moment of inertia of a solid body about an axis in 3-space relates the angular acceleration about this axis to torque (force twisting the body). The moments of inertia about the coordinate axes of a body of constant density and mass $m$ occupying a region $W$ of volume $V$ are defined to be $$I_x = \frac{m}{V}\int_W (y^2+z^2) \,dV\qquad I_y = \frac{m}{V}\int_W (x^2+z^2) \,dV\qquad I_z = \frac{m}{V}\int_W (x^2+y^2) \,dV$$ Use these definitions to find the moment of inertia about the $z$-axis of the rectangular solid of mass $18$ given by $0 \le x \le 2$, $0 \le y \le 3$, $0 \le z \le 1$.

$I_x =$
$I_y =$
$I_z =$