Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.2 Arc Length and Speed - Exercises - Page 610: 2

$$6\sqrt{5}$$

\begin{aligned} s &=\int_{a}^{b} \sqrt{x^{\prime}(t)^{2}+y^{\prime}(t)^{2}} d t \\ &=\int_{1}^{4} \sqrt{4+16} d t \\ &=\int_{1}^{4} \sqrt{20} d t \\ &=\int_{1}^{4} 2 \sqrt{5} d t \\ &=\left.2 \sqrt{5} t\right|_{1} ^{4}\\ &=6\sqrt{5} \end{aligned}