Find $\mathbf { r } ( t )$ If $\mathbf { r } ^ { \prime } ( t ) = \sin t \mathbf { i } - \cos t \mathbf { j } + 6 t \mathbf { k }$

Find $\mathbf { r } ( t )$ if $\mathbf { r } ^ { \prime } ( t ) = \sin t \mathbf { i } - \cos t \mathbf { j } + 6 t \mathbf { k }$ and $r ( 0 ) = i + j + 5 k$ .

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

Correct Answer:

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