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Recently, I came across a closed form solution to ∫|cos(x)|dx as

sin(x-∏*floor(x/∏+1/2)) + 2*floor(x/∏+1/2)

I have no idea how to reach this solution but checking this for definite integral from 0 to 3∏/4 or ∏ seems to work. Using |cos(x)| as cos(x)*sgn(cos(x)) doesn't help in reaching at the solution. Does someone know how to get this closed form?

Thanks.

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# Closed form integral of abs(cos(x))

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