Answer
$\approx 8.617$
Work Step by Step
Since, $L=\int_{0}^{\pi/2}\sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dt})^2}dt$
Thus, $L=\int_{0}^{1} (3\sqrt 2)t \sqrt{16+t^2} dt$
Plug $16+t^2=u \implies du=2tdt$
Then, we have $L=(\dfrac{3\sqrt 2}{2})\int_{16}^{17} \sqrt{p} dp=(\dfrac{3\sqrt 2}{2}) [(2/3)u^{3/2}]_{16}^{17}$
Thus, $L \approx 8.617$
