Chapter 9 - Further Applications of the Integral and Taylor Polynomials - Chapter Review Exercises - Page 496: 3

$$4\sqrt{17}$$

Given $$y=4 x-2, \quad[-2,2] $$ Since $$y' = 4 $$ Then the arc length is given by \begin{aligned} s&=\int_{a}^{b} \sqrt{1+\left(y^{\prime}\right)^{2}} d x \\ &=\int_{-2}^{2} \sqrt{1+16} d x \\ &=\int_{-2}^{2} \sqrt{17} d x\\ &=\sqrt{17}x\bigg|_{-2}^{2}\\ &= 4\sqrt{17} \end{aligned}