Answer
$4\sqrt 3$
Work Step by Step
Here,we have
$L=\int_{m}^{n}\sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dt})^2}dt$
This gives:
$L=\int_{-\sqrt 3}^{\sqrt 3}\sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dt})^2}dt=\int_{-\sqrt 3}^{\sqrt 3} \sqrt{(t^2+1)^2} dt$
This implies that
$L=[\dfrac{t^3}{3}+t]_{-\sqrt 3}^{\sqrt 3}=4\sqrt 3$