Answer
$ \dfrac{10}{3}$
Work Step by Step
Integrate the integral to calculate the arc length as follows:
$l= \int_{A}^{B} \sqrt {1+(\dfrac{dy}{dx})^2}$
or, $ =\int_{1}^{4} \sqrt {1+\dfrac{1}{4} (x^{-1} -2+x)} dx$
or, $=0.5 [2x^{1/2} +\dfrac{2x^{3/2}} {3}]_1^4$
or, $ = \dfrac{10}{3}$
