Question Number 169855 by Shrinava last updated on 11/May/22
Answered by thfchristopher last updated on 11/May/22
![=∫_0 ^(π/4) sin (3x−x)dx =∫_0 ^(π/4) sin 2xdx −(1/2)[cos 2x]_0 ^(π/4) (1/2)](Q169857.png)
$$=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \mathrm{sin}\:\left(\mathrm{3}{x}−{x}\right){dx} \\ $$$$=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \mathrm{sin}\:\mathrm{2}{xdx} \\ $$$$−\frac{\mathrm{1}}{\mathrm{2}}\left[\mathrm{cos}\:\mathrm{2}{x}\right]_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}} \\ $$