Question Number 115363 by mathdave last updated on 25/Sep/20
$${evaluate} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{3}}} \frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{2}} {x}+\mathrm{cos}^{\mathrm{2}} {x}}{dx} \\ $$
Answered by Dwaipayan Shikari last updated on 25/Sep/20
$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{3}}} \frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{2}} \mathrm{x}+\mathrm{cos}^{\mathrm{2}} \mathrm{x}}\mathrm{dx}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{3}}} \mathrm{1dx}=\frac{\pi}{\mathrm{3}} \\ $$