A rod of variable density

A long, thin rod of length L has a linear mass density λ given by the euqation above, where x = 0 at the left end of the rod, and x = L at the right end of the rod.

1. What is the mass of the rod, in terms of L?
2. Where is the center of mass of the rod, in terms of L? Does this make sense?
3. What is the moment of inertia of the rod, in terms of L?

Suppose that L = 2 m.

1. What is the mass of the rod?
2. Where is the center of mass of the rod? Does this make sense?
3. What is the moment of inertia of the rod?