$$\text { Find the required quantity given the wire that lies along the curve } r \text { and has density } \delta .$$

Multiple Choice

$$\text { Find the required quantity given the wire that lies along the curve } r \text { and has density } \delta .$$
-Moment of inertia $\mathrm { I } _ { \mathrm { Z } }$ about the $\mathrm { z }$ -axis, where $r ( t ) = ( 4 \sin 3 t ) i + ( 4 \cos 3 t ) j + e ^ { 2 t } k , 0 \leq t \leq 1 ; \delta ( x , y , z ) = z ^ { 2 }$

A) $I _ { Z } = \frac { 2 } { 3 } \left[ \left( 144 + 4 e ^ { 4 } \right) ^ { 3 / 2 } - ( 144 + 4 ) ^ { 3 / 2 } \right]$
B) $\mathrm { I } _ { \mathrm { Z } } = \frac { 8 } { 3 } \left( \mathrm { e } ^ { 4 } - 1 \right)$
C) $\mathrm { I } _ { \mathrm { Z } } = \frac { 4 } { 3 }$
D) $\mathrm { I } _ { \mathrm { Z } } = \frac { 2 } { 3 }$