Vector Calculus · Challenge problem

Let $C$ be the arc of the parabola $y = 4 - x^2$ with $y\ge 0$, and let $\mathbf n$ be its unit normal pointing away from the origin. Find the flux $\displaystyle\int_C\mathbf F\cdot\mathbf n\,ds$ of the source field $\mathbf F = \dfrac{(x,\; y)}{x^2 + y^2}$ across $C$. Give your answer in terms of $\pi$.