The Moment of Inertia of a Lamina in the Shape $x ^ { 2 } + y ^ { 2 } = 1 , y \geq 0$

Multiple Choice

The moment of inertia of a lamina in the shape of a region in the xy-plane bounded by $x ^ { 2 } + y ^ { 2 } = 1 , y \geq 0$ and the x-axis with area density $\rho ( x , y ) = y$ about the x-axis is

A) 13
B) 9
C) $\frac { 65 } { 8 }$
D) $\frac { 4 } { 15 }$
E) $\frac { 1 } { 15 }$