A thin-walled hollow cone has uniform density with thickness t1 at the left-hand end and...

A thin-walled hollow cone has uniform density with thickness t₁ at the left-hand end and t₂ at the right-hand end.

(a) If the cone’s thickness varies linearly from t₁ = 2t₀ at the left-hand end to t₂ = t₀ at the right-hand end, fully set up the integral, including limits of integration, that will yield the mass moment of inertia about the x axis.

(b) Evaluate the integral obtained in Part (a) using computer software such as Mathematica or Maple. Express your answer in terms of the mass m of the object.