I am required to prove that $\displaystyle \int_0^{2\pi} |x \cos(\theta)+y \sin(\theta)|\, d\theta= 4\sqrt{x^2+y^2}$, $\ x$ and $y$ are real.
I let $\sin\theta = \frac yz$, $\cos\theta=\frac xz$, where $z$ is supposedly complex. Then i managed to show that $x\cos\theta + y\sin\theta = z$, so i am left with integrating $|z|$ (which is the area of a circle?)
I am stuck here since the RHS of what i am supposed to prove, doesn't have pi inside.
Please advise, thanks!!