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

Multiple Choice

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

A) $\frac { 52 \pi } { 3 }$
B) $\frac { 26 \pi } { 3 }$
C) $\frac { 13 \pi } { 3 }$
D) $\frac { 11 \pi } { 5 }$
E) $\frac { 8 \pi } { 3 }$