Find the Arc Length of the Curve on the Given $x = t ^ { 2 } , y = 8 t , 0 \leq t \leq 4$

Find the arc length of the curve on the given interval. $x = t ^ { 2 } , y = 8 t , 0 \leq t \leq 4$

A) $4 ( \sqrt { 2 } + \ln \sqrt { 2 } + \ln ( 2 + \sqrt { 2 } ) )$
B) $4 ( \sqrt { 2 } - \ln \sqrt { 2 } + \ln ( 2 + \sqrt { 2 } ) )$
C) $4 ( \sqrt { 2 } + \ln ( 2 + \sqrt { 2 } ) )$
D) $16 ( \sqrt { 2 } - \ln \sqrt { 2 } + \ln ( 2 + \sqrt { 2 } ) )$
E) $16 ( \sqrt { 2 } + \ln \sqrt { 2 } + \ln ( 2 + \sqrt { 2 } ) )$