The Area of the Surface Generated by Revolving the Curve $x ( t ) = t , \quad y ( t ) = t ^ { 2 }$

Multiple Choice

The area of the surface generated by revolving the curve $x ( t ) = t , \quad y ( t ) = t ^ { 2 }$ with $t \in [ 0,2 ]$ about the y-axis is

A) $\frac { \pi ( 17 \sqrt { 17 } - 1 ) } { 2 }$
B) $\frac { \pi ( 17 \sqrt { 17 } + 1 ) } { 3 }$
C) $\frac { \pi ( 17 \sqrt { 17 } - 1 ) } { 3 }$
D) $\frac { \pi ( 17 \sqrt { 17 } + 1 ) } { 6 }$
E) $\frac { \pi ( 17 \sqrt { 17 } - 1 ) } { 6 }$