Question Number 123509 by Jamshidbek2311 last updated on 26/Nov/20
$$\underset{−\frac{\pi}{}\mathrm{2}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\mid{cosx}\mid=? \\ $$
Answered by bramlexs22 last updated on 26/Nov/20
![= ∫_(−π/2) ^(π/2) ∣cos x∣ dx = 2∫_0 ^(π/2) cos x dx = 2(sin x)]_0 ^(π/2) = 2](https://www.tinkutara.com/question/Q123512.png)
$$=\:\underset{−\pi/\mathrm{2}} {\overset{\pi/\mathrm{2}} {\int}}\mid\mathrm{cos}\:{x}\mid\:{dx}\:=\:\mathrm{2}\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\mathrm{cos}\:{x}\:{dx} \\ $$$$\left.=\:\mathrm{2}\left(\mathrm{sin}\:{x}\right)\right]_{\mathrm{0}} ^{\pi/\mathrm{2}} \:=\:\mathrm{2} \\ $$