# How to evaluate $\int_0^{2\pi}|\sin(x)\cos(x)|\,\mathrm dx$ [closed]

I would like to know how to evaluate this integral:

$$\int_0^{2\pi} |\sin (x) \cos (x)| \, \mathrm dx$$

I know it is equal to 2.

## closed as off-topic by Martin R, cmk, mrtaurho, A. Goodier, Adrian KeisterJul 10 at 14:08

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## 1 Answer

Hints: Since $$\bigl\lvert\sin(x)\cos(x)\bigr\rvert=\frac12\bigl\lvert\sin(2x)\bigr\rvert$$ is a periodic function with period $$\frac\pi2$$, your integral is equal to$$2\int_0^{\frac\pi2}\bigl\lvert\sin(2x)\bigr\rvert\,\mathrm dx.$$And $$\sin(2x)$$ is non-negative on $$\left[0,\frac\pi2\right]$$.