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Wire of constant density $\quad$ A wire of constant density $\delta = 1$ lies along the curve

$$

\mathbf { r } ( t ) = ( t \cos t ) \mathbf { i } + ( t \sin t ) \mathbf { j } + ( 2 \sqrt { 2 } / 3 ) t ^ { 3 / 2 } \mathbf { k } , \quad 0 \leq t \leq 1

$$

Find $\overline { z }$ and $I _ { z }$

$\frac{7}{12}$

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University of Illinois at Urbana-Champaign