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

Multiple Choice

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

A) $\mathrm { I } _ { \mathrm { y } } = - \frac { 1600 } { 3 }$
B) $\mathrm { I } _ { \mathrm { y } } = - \frac { 320 } { 3 }$
C) $\mathrm { I } _ { \mathrm { y } } = \frac { 320 } { 3 }$
D) $\mathrm { I } _ { \mathrm { y } } = \frac { 1600 } { 3 }$