Find the Length of the Indicated Portion of the Curve $$r ( t ) = \left( e ^ { t } \cos t \right) i + \left( e ^ { t } \sin t \right) j + 7 e ^ { t } k ^ { \prime } , - \ln 2 \leq t \leq 0$$

Multiple Choice

Find the length of the indicated portion of the curve.
- $$r ( t ) = \left( e ^ { t } \cos t \right) i + \left( e ^ { t } \sin t \right) j + 7 e ^ { t } k ^ { \prime } , - \ln 2 \leq t \leq 0$$

A) $\frac { \sqrt { 47 } } { 2 }$
B) $\frac { \sqrt { 51 } } { 2 }$
C) $\frac { \sqrt { 47 } } { 4 }$
D) $\frac { \sqrt { 51 } } { 4 }$