Consider the rectangular region with vertices in $($distance in $[$m$])$

$(0,1)$

$(3,1)$

$(3,3)$

$(0,3)$

The region is a lamina and has a density $k\frac{g}{m^2}$ model defined by

$(x,y)=x^{2}y$

Find

a$)$ The $x$ upper and lower integration limit$,$ in $[$m$]$

b$)$ The $y$ upper and lower integration limit$,$ in $[$m$]$

c$)$ The mass, $m$ in $kg$

d$)$ The momentum of mass about the x $-$axis, $M_x$ in $kg*m$

e$)$ The momentum of mass about the y $-$axis, $M_y$ in $kg*m$

f$)$ The $x-$coordinate of the center of mass, $\stackrel{}{x}$ in $[$m$]$

g$)$ The $y-$coordinate of the center of mass, $\frac{?}{\text{b}\text{a}\text{r}}(y)$ in $[$m$]$

h$)$ The momentum of inertia about the x $-$axis, $I_x$ in $kg*m^2$

i$)$ The momentum of inertia about the y $-$axis, $I_y$ in $kg*m^2$

j$)$ The momentum of inertia about the origin, $I_0$ in $kg*m^2$