Find the Moment of Inertia $I _ { x }$ Of the Lamina That Occupies the Region

Multiple Choice

Find the moment of inertia $I _ { x }$ of the lamina that occupies the region $D = \{ ( x , y ) \mid 0 \leq x \leq 1,0 \leq y \leq 1 \}$ and has density function $p ( x , y ) = x$ .

A) $\frac { 1 } { 24 }$

B) $\frac { 1 } { 18 }$
C) $\frac { 1 } { 12 }$
D) $\frac { 1 } { 9 }$
E) $\frac { 1 } { 6 }$
F) $\frac { 1 } { 4 }$

G) $\frac { 1 } { 3 }$

H) $\frac { 1 } { 2 }$