The Length of the Curve $x ( t ) = e ^ { t } \cos t , y ( t ) = e ^ { t } \sin t$

Multiple Choice

The length of the curve $x ( t ) = e ^ { t } \cos t , y ( t ) = e ^ { t } \sin t$ with $t \in [ 0 , \pi ]$ is

A) $\sqrt { 3 } \left( e ^ { \pi } - 1 \right)$
B) $\sqrt { 3 } \left( e ^ { \pi } + 1 \right)$
C) $\sqrt { 5 } \left( e ^ { \pi } - 1 \right)$
D) $\sqrt { 2 } \left( e ^ { \pi } + 1 \right)$
E) $\sqrt { 2 } \left( e ^ { \pi } - 1 \right)$