The Length of the Curve $x ( t ) = 9 - t ^ { 3 } , y ( t ) = t ^ { 2 }$

Multiple Choice

The length of the curve $x ( t ) = 9 - t ^ { 3 } , y ( t ) = t ^ { 2 }$ with $t \in [ 0,2 ]$ is

A) $\frac { 8 ( 10 \sqrt { 10 } - 1 ) } { 3 }$
B) $\frac { 8 ( 10 \sqrt { 10 } - 1 ) } { 18 }$
C) $\frac { 8 ( 10 \sqrt { 10 } - 1 ) } { 36 }$
D) $\frac { 8 ( 10 \sqrt { 10 } - 1 ) } { 9 }$
E) $\frac { 8 ( 10 \sqrt { 10 } - 1 ) } { 27 }$