I was working on the problem attached in the image below, which asks to calculate the integral over the closed path in the figure. The integral is $$\oint \vec A \cdot d\vec l $$ where $\vec A = r\cos\phi\,\hat{r} + \sin\phi\,\hat{\phi}$. So I tried letting the vector be in the original form and tried to come up with an equation for the path in polar coordinates. I found the arclength but I'm not able to make it work. Or should I try to switch the vector into cartesian coordinates? Any help is welcomed!
The image:
