The Area of the Surface Generated by Revolving the Curve $x ( t ) = 4 t , \quad y = t ^ { 2 } - 2 \ln t$

Multiple Choice

The area of the surface generated by revolving the curve $x ( t ) = 4 t , \quad y = t ^ { 2 } - 2 \ln t$ with $t \in [ 0,1 ]$ about the y-axis is

A) $\frac { 2 \pi } { 3 }$
B) $\frac { 4 \pi } { 3 }$
C) $\frac { 8 \pi } { 3 }$
D) $\frac { 16 \pi } { 3 }$
E) $\frac { 64 \pi } { 3 }$