A slender $0\mathrm{.}65-$m long rod has a mass per unit length that varies with distance from the left

end, where x $=0,$ according to dm$/$dx $=(280+360$x$2)$ g$/$m$.($a$)$ Calculate the total mass of the rod.

$($b$)$ Find the location of the rod's center of mass. $($c$)$ Calculate the moment of inertia of the rod for an axis at the left end, perpendicular to the rod.