A throwing toy is molded of uniform foam. It consists of an oblong-shaped portion, a cyl...

A throwing toy is molded of uniform foam. It consists of an oblong-shaped portion, a cylindrical portion, and four rectangular fins The density of the oblong and cylindrical shapes is 100 kg/m³, and each of the fin have 1.8×10⁻³ kg mass.

(a) Fully set up the integral, including limits of integration, that will yield the mass moment of inertia about the x axis for the oblong-shaped portion.

(b) Evaluate the integral obtained in Part (a) using computer software such as Mathematica or Maple.

(c) You should fin the result of Part (b) to be 79.8 kg.mm². Using this value, determine the total mass moment of inertia about the x axis for the toy.