/sci/ - Science & Math

Hey /sci/, got a problem that I don't quite understand how to solve. So for Calc 2, I'm required to do homework on MyMathLab and I came across a problem on Total Distance traveled.

Lemme give you the important shit.

v(t) = 4cos(2t) on the interval [0, 2π]

Positive on: [0, π/4], [3π/4, 5π/4], and [7π/4, 2π]

Negative on: [π/4, 3π/4] and [5π/4, 7π/4]

So, I already know that I need to use absolute values in order to find the total distance for ∫ |v(t) dt on [0, 2π] BUT, that will take up too much time to calculate and too much space. Couldn't I just integrate v(t) from [0, π/4] and then multiply the result 5 times as opposed to calculating the whole damn thing?