Question Number 8806 by tawakalitu last updated on 28/Oct/16
$$\int_{\frac{\pi}{\mathrm{4}}} ^{\pi} \mathrm{cos2x}\:\mathrm{dx} \\ $$
Commented by ridwan balatif last updated on 29/Oct/16
$$\int_{\frac{\pi}{\mathrm{4}}} ^{\pi} \mathrm{cos2x}\:\mathrm{dx}=\:\frac{\mathrm{1}}{\mathrm{2}}×\left(\mathrm{sin2x}\right)\underset{\frac{\pi}{\mathrm{4}}} {\overset{\pi} {\mid}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{1}}{\mathrm{2}}×\left(\mathrm{sin2}\pi−\mathrm{sin}\pi/\mathrm{2}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{1}}{\mathrm{2}}×\left(\mathrm{0}−\mathrm{1}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$
Commented by tawakalitu last updated on 29/Oct/16
$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{sir}. \\ $$