Answer
$\pi-2-2\sqrt 2$
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
$\int_C f(x,y) ds=(4) \int_{\pi/4}^{\pi/2} 2\cos^ t-\sin t dt$
Thus, we have
$ 4[\dfrac{1}{2}\sin 2t+\cos t+t]_{\pi/4}^{\pi/2}=\pi-2-2\sqrt 2$
