Find $\mathbf { r } ( t )$ Satisfying the Conditions For

Multiple Choice

Find $\mathbf { r } ( t )$ satisfying the conditions for $\mathbf { r } ^ { \prime } ( t ) = 5 \mathbf { i } + 8 t \mathbf { j } - 6 t ^ { 2 } \mathbf { k }$ $\mathbf { r } ( 0 ) = \mathbf { i } + \mathbf { j }$

A) $( 5 t + 1 ) \mathbf { i } + \left( 4 t ^ { 2 } + 1 \right) \mathbf { j } - 2 t ^ { 3 } \mathbf { k }$
B) $( 5 t + 1 ) \mathbf { i } + \left( 8 t ^ { 2 } + 1 \right) \mathbf { j } - 6 t ^ { 3 } \mathbf { k }$
C) $5 t \mathbf { i } + 4 t ^ { 2 } \mathbf { j } - 2 t ^ { 3 } \mathbf { k }$
D) $5 t \mathbf { i } + 8 t ^ { 2 } \mathbf { j } - 6 t ^ { 3 } \mathbf { k }$