$$\text { Find the mass of the wire that lies along the curve } r \text { and has density } \delta \text {. }$$

Multiple Choice

$$\text { Find the mass of the wire that lies along the curve } r \text { and has density } \delta \text {. }$$
- $$C _ { 1 } : \mathbf { r } ( t ) = ( 5 \cos t ) \mathbf { i } + ( 5 \sin t ) \mathbf { j } , 0 \leq t \leq \frac { \pi } { 2 } \text {; }$$
$C _ { 2 } : \mathbf { r } ( \mathrm { t } ) = 5 \mathrm { j } + \mathrm { tk } , 0 \leq \mathrm { t } \leq 1 ; \delta = 8 \mathrm { t } ^ { 3 }$

A) $2 \left( \frac { 1 } { 16 } \pi ^ { 3 } + 1 \right)$ units
B) $\frac { 5 } { 6 } \pi ^ { 3 }$ units
C) $2 \left( \frac { 5 } { 16 } \pi ^ { 4 } + 1 \right)$ units
D) $\frac { 20 } { 3 } \pi ^ { 3 }$ units