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If a wire with linear density $ \rho(x, y, z) $ lies along a space curve $ C $, its $ \textbf{moments of inertia} $ about the $ x $-, $ y $-, and $ z $-axes are defined as

$$ I_x = \int_C (y^2 + z^2) \rho(x, y, z) ds $$

$$ I_y = \int_C (x^2 + z^2) \rho(x, y, z) ds $$

$$ I_z = \int_C (x^2 + y^2) \rho(x, y, z) ds $$

Find the moments of inertia for the wire in Exercise 35.

$$

\begin{array}{c}{I_{x}=I_{y}=4 \sqrt{13} k \pi\left(1+6 \pi^{2}\right)} \\ {I_{z}=8 \sqrt{13} k \pi}\end{array}

$$

Vector Calculus

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Missouri State University

Harvey Mudd College

Baylor University

Boston College

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