Tính tích phân

C

- Hướng dẫn giải

Chọn C.

Nếu: $\frac{\mathrm{\pi }}{4}\le x\le \frac{\mathrm{\pi }}{2}\iff \frac{{\displaystyle \mathrm{\pi }}}{{\displaystyle 2}}\le 2x\le \mathrm{\pi }\Rightarrow \sin 2\mathrm{x}\ge 0$

Nếu: $\frac{\mathrm{\pi }}{2}\le x\le \frac{3\mathrm{\pi }}{4}\iff \mathrm{\pi }\le 2x\le \frac{3\mathrm{\pi }}{2}\Rightarrow \sin 2\mathrm{x}\le 0$

Khi đó: 

$I={\int }_{\frac{\mathrm{\pi }}{4}}^{\frac{3\mathrm{\pi }}{4}}\left|\sin 2x\right|dx={\int }_{\frac{\mathrm{\pi }}{4}}^{\frac{\mathrm{\pi }}{2}}\sin 2xdx-{\int }_{\frac{\mathrm{\pi }}{2}}^{\frac{3\mathrm{\pi }}{4}}\sin 2xdx$