Answer
$\dfrac{285}{3}$
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}^{32} \sqrt {\dfrac{(x^{2/5}+2+x^{-2/5})}{4}} dy$
or, $=\dfrac{1}{2} [\dfrac{5}{6} x^{6/5} +\dfrac{5}{4} x^{4/5} ]_{1}^{32} $
or, $= \dfrac{1}{2} (\dfrac{315}{6}+\dfrac{75}{4})$
or, $=\dfrac{285}{3}$
