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

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.

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If you just need the result without derivation: wolframalpha.com/input/?i=laplace+transform+abs%28cos%28x%29%29 –  in_wolframAlpha_we_trust Jun 14 '12 at 9:46
I see there is a formula for your function. –  Babak S. Jun 14 '12 at 9:46
@in_wolfram_we_trust: Make me a detailed hint. –  Nancy Rutkowskie Jun 14 '12 at 9:48
Sorry, I don't have one. –  in_wolframAlpha_we_trust Jun 14 '12 at 9:49
But You can look at @BabakSorouh answer below. –  in_wolframAlpha_we_trust Jun 14 '12 at 9:57

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 $\frac{\pi}{2}$.
Nice!! :+) $\quad +1 \quad$ –  amWhy Mar 6 '13 at 0:54