Need physics help with non-uniform rod inertia and KE

A thin rod of length L = 2.85 m lies along the x-axis with one end at the origin. The rod has a non-uniform density given by λ(x) = γx3, where γ = 0.50 kg/m4.

Find the total mass of the rod.
M = _____kg

Find the location of the center of mass of the rod.
XCM = _____m

Find the moment of inertia of the rod about an axis passing through the center of mass of the rod.
I = _______kg-m2

If the rod is spinning about an axis through the center of mass with angular speed ω = 5.00 rad/s, what is the kinetic energy of the rod?
K =______ J

 
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