Problem $5.$ Consider the area between two curves as shown in the figure.

a$)$ Find the location of the centroid

b$)$ Find the moment of inertia about $x($i$.$e$.,I_x).$

c$)$ Find the moment of inertia about y $($i$.$e$.,I_y).$

d$)$ Find the mixed moment of inertia $($i$.$e$.,I_{xy}).$

e$)$ Find the moments of inertia about the centroidal axis.

f$)$ Find the polar moment of inertia $($i$.$e$.,$ moment of inerti; about O $).$