Every day, Naranath
starts from the bottom of a valley and pushes his boulder all the way up to the summit of a mountain. He then lets it roll all the way back down the mountain and laughs thunderously.
\[f(x) = \cos^5(x) + 1, x \in [-\pi, \pi]\]
...represents the height of the mountain at a given point. How far does the boulder roll every day?
Details and assumptions:
- The boulder stops as soon as it hits the bottom of the valley; it doesn't roll any further.
- Round to the hundredth's place.