Find the Arc Length Function $s ( t )$ For the Curve Defined By

Essay

Find the arc length function $s ( t )$ for the curve defined by $\mathbf { r } ( t ) = e ^ { 2 t } \cos t \mathbf { i } + e ^ { 2 t } \sin t \mathbf { j } + e ^ { 2 t } \mathbf { k }$ for $t \geq 0$ . Then use this result to find a parametrization of $C$ in terms of $s$ .