Finding the Laplace transform of $f(x)=|\cos(x)|$

Question

I have function $f(x)=|\cos(x)|, x≥0$ and like to derive its Laplace transform. I am told that $f(x+\pi)=f(x)$. Help me please.

Answer 1

Your function is periodic ($T=\pi$) so you can easily use the formula:

$L(f(x))=\frac{1}{1-e^{-sT}}\int_{0}^{T}e^{-sT}f(x)dx$

Note that your function is a piecewise function broken at $\frac{\pi}{2}$.