Menu Close

Category: Integration

Question-172510

Question Number 172510 by Mikenice last updated on 28/Jun/22 Answered by mr W last updated on 28/Jun/22 $${e}^{\frac{{x}}{\mathrm{2}}} {x}=\pm\sqrt{\mathrm{2}} \\ $$$${e}^{\frac{{x}}{\mathrm{2}}} \left(\frac{{x}}{\mathrm{2}}\right)=\pm\frac{\sqrt{\mathrm{2}}}{\mathrm{2}} \\ $$$$\frac{{x}}{\mathrm{2}}={W}\left(\pm\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\right) \\…

let-f-a-0-pi-dx-a-cos-2-x-with-a-gt-0-1-explicite-f-a-2-explicite-g-a-0-pi-dx-a-cos-2-x-2-3-find-tbe-valued-of-intevrsls-0-pi-dx-1-cos-2-x-and-0-pi-dx-1-cos-2-x-

Question Number 106948 by abdomathmax last updated on 08/Aug/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{a}\right)\:=\int_{\mathrm{0}} ^{\pi} \:\frac{\mathrm{dx}}{\mathrm{a}+\mathrm{cos}^{\mathrm{2}} \mathrm{x}}\:\mathrm{with}\:\mathrm{a}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{explicite}\:\mathrm{f}\left(\mathrm{a}\right) \\ $$$$\left.\mathrm{2}\right)\mathrm{explicite}\:\mathrm{g}\left(\mathrm{a}\right)\:=\int_{\mathrm{0}} ^{\pi} \:\:\frac{\mathrm{dx}}{\left(\mathrm{a}+\mathrm{cos}^{\mathrm{2}} \mathrm{x}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:\mathrm{find}\:\mathrm{tbe}\:\mathrm{valued}\:\mathrm{of}\:\mathrm{intevrsls} \\ $$$$\int_{\mathrm{0}}…