Question Number 64225 by mmkkmm000m last updated on 16/Jul/19
$$\mathrm{Solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\underset{\:\sqrt{\mathrm{2}}} {\overset{{x}} {\int}}\:\:\:\frac{{dx}}{{x}\:\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}\:=\:\frac{\pi}{\mathrm{12}}\:\:\mathrm{is}\:\:{x}\:=\:\_\_\_\_\_. \\ $$
Answered by ajfour last updated on 16/Jul/19
$$\mathrm{cos}^{−\mathrm{1}} \frac{\mathrm{1}}{{x}}−\frac{\pi}{\mathrm{4}}=\frac{\pi}{\mathrm{12}} \\ $$$$\Rightarrow\:\:\frac{\mathrm{1}}{{x}}=\mathrm{cos}\:\frac{\pi}{\mathrm{3}}\:\:\Rightarrow\:\:{x}=\mathrm{2}\:. \\ $$