The Arc Length Of $y = \ln ( \sec x ) \text { for } x \in \left[ 0 , \frac { \pi } { 4 } \right]$

Multiple Choice

The arc length of $y = \ln ( \sec x ) \text { for } x \in \left[ 0 , \frac { \pi } { 4 } \right]$ is

A) $\frac { \ln ( 3 - 2 \sqrt { 2 } ) } { 2 }$
B) $\frac { \ln ( 3 + \sqrt { 2 } ) } { 2 }$
C) $\frac { \ln ( 3 + 2 \sqrt { 2 } ) } { 2 }$
D) $\frac { \ln ( 3 - \sqrt { 2 } ) } { 2 }$
E) $\frac { \ln ( 3 - \sqrt { 2 } ) } { 2 }$ .