Answer
$$4\pi$$
Work Step by Step
Since $ds=\sqrt {(\dfrac{dx}{dt})^2+(\dfrac{dy}{dt})^2} dt$
We have: $x=2 \cos \theta \implies \dfrac{dx}{dt}=-2\sin \theta$
and $y=2 \sin \theta \implies \dfrac{dy}{dt}=2 \cos \theta$
So, $ds=\sqrt {(2 \cos \theta)^2+(-2 \sin \theta)^2} dt=2 \ dt$
We need to re-write the line integral in terms of $t$ to simplify the integral by using parametric equations.
Now, the line integral is:
$\int_C (x^2+y^2) ds=2 \times \int_0^{\pi/2} (4) dt \\=[8t]_0^{\pi/2}\\=\dfrac{8\pi}{2}\\=4\pi$
