I have this function $$f(x)=-11 \cos x+11 \cos 2 x+6$$ with period $2\pi$. The plot of function is on the left below. Then, I want to know how I can calculate the lengths of the four arcs for which $-2<f(x)<6$ that is the plot on the right. Any comments or hints are appreciated.
If we have a curve, $y=f(x)$, then the length of the curve between $x=a$ and $x=b$ is equal $$\int_a^b\sqrt{\left(\frac{dy}{dx}\right)^2+1}~dx$$ Does that help?