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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.

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

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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 $\left[0,\frac\pi2\right]$.

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