Answer
$8$
Work Step by Step
Here, we have
$ ds=\sqrt {(\dfrac{dx}{dt})^2+(\dfrac{dy}{dt})^2+(\dfrac{dz}{dt})^2} dt$
and $ds= 2dt$
This implies that
$L=(4) \int_{0}^{\pi/2} \cos t+\sin t dt$
Thus, we have
$ 4[\sin t-\cos t]_{0}^{\pi/2}=8$