The Moment of Inertia of a Lamina in the Shape $x = 3 , y = 2 , x = 0$

Multiple Choice

The moment of inertia of a lamina in the shape of a region in the xy-plane bounded by $x = 3 , y = 2 , x = 0$ and the x-axis with area density $\rho ( x , y ) = x y ^ { 2 }$ about the y-axis is

A) 54
B) 48
C) 45
D) 42
E) 38