Moments of Inertia Consider a wire of density (x, y) given by the space curve The moments

Moments of Inertia Consider a wire of density ρ(x, y) given by the space curve

The moments of inertia about the x- and y-axes are given by

Find the moments of inertia for the wire of density ρ.

A wire lies along r(t) = a cos ti + a sin tj, where 0 ≤ t ≤ 2π and a > 0, with density ρ(x, y) = y.

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C: r(t) = x(t)i + y(t)j, 0 ≤ t ≤b.