Answer
$8$
Work Step by Step
We set up the integral:
$$\int_{C} f(x, y, z) d s=\int_{a}^{b} f(g(t), h(t), k(t))|\mathbf{v}(t)| d t$$
Where
$$f=x+y$$ and $$\mathbf{r}(t)=2\cos{t} \mathbf{i}+2\sin{t}\mathbf{j}$$ and the $t$ range is $$0 \leq t \leq \frac{\pi}{2}$$ Since we are considering the first octant of the circle, we have: $$x^2+y^2=4$$
Thus:
$$\int_{0}^{\pi/2} 2(\cos t + \sin t) \sqrt{4} dt = 4(\sin{\pi/2}-\cos{\pi/2}-\sin{0}+\cos{0})=4(1-0-0+1)=8$$
