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 Keister Jul 10 at 14:08

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Martin R, cmk, mrtaurho, A. Goodier, Adrian Keister
If this question can be reworded to fit the rules in the help center, please edit the question.


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


Not the answer you're looking for? Browse other questions tagged or ask your own question.