Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.2 Arc Length and Speed - Exercises - Page 610: 1

$$10$$

\begin{aligned} s &=\int_{a}^{b} \sqrt{x^{\prime}(t)^{2}+y^{\prime}(t)^{2}} d t \\ &=\int_{0}^{2} \sqrt{9+16} d t \\ &=\int_{0}^{2} \sqrt{25} d t \\ &=\int_{0}^{2} 5 d t \\ &= 5 t\bigg|_{0} ^{2}\\ &=10 \end{aligned}