Answer
$ \dfrac{10}{3}$
Work Step by Step
Our aim is to integrate the integral in order to find the arc length.
$$L= \int_{p}^{q} \sqrt {1+(y')^2}$$ $$ \\=\int_{1}^{4} \sqrt {1+\dfrac{1}{4} (\dfrac{1}{x} -2+x)} dx \\=0.5 [2\sqrt x +\dfrac{2x^{(3/2)}} {3}]_1^4 \\ = \dfrac{10}{3}$$
