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.
2026-03-29 03:28:09.1774754889
How to evaluate $\int_0^{2\pi}|\sin(x)\cos(x)|\,\mathrm dx$
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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 $\left[0,\frac\pi2\right]$.