Category: Integration

Question Number 39135 by maxmathsup by imad last updated on 02/Jul/18 $${calculate}\:{A}\left(\lambda\right)\:=\:\int_{\mathrm{0}} ^{\lambda} \:\:\:\frac{{ln}\left({x}+\sqrt{\left.\mathrm{1}+{x}^{\mathrm{2}} \right)}\right.}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:{dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left({x}+\sqrt{\left.\mathrm{1}+{x}^{\mathrm{2}} \right)}\right.}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{dx} \\ $$ Commented…

Question Number 39120 by math khazana by abdo last updated on 02/Jul/18 $${let}\:{A}_{{n}} =\:\int_{\mathrm{1}} ^{{n}} \:\frac{\left[\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right]\:−\left[{x}\right]}{{x}^{\mathrm{2}} }\:{dx}\:\:\left({n}\:{integr}\:\geqslant\mathrm{1}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \: \\…

Question Number 104644 by Rohit@Thakur last updated on 22/Jul/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{log}\left(\mathrm{1}−{x}+{x}^{\mathrm{2}} −{x}^{\mathrm{3}} +{x}^{\mathrm{4}} \right){dx}}{{x}}\:=\:−\frac{\pi^{\mathrm{2}} }{\mathrm{15}} \\ $$ Answered by mathmax by abdo last updated…

Question Number 104609 by  M±th+et+s last updated on 22/Jul/20 $${prove}: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{\mathrm{4}} \left(\mathrm{1}−{x}\right)^{\mathrm{4}} }{\mathrm{1}+{x}^{\mathrm{2}} }{dx}=\frac{\mathrm{22}}{\mathrm{7}}−\pi \\ $$ Answered by Dwaipayan Shikari last updated…

Question Number 39040 by maxmathsup by imad last updated on 01/Jul/18 $${find}\:{F}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\pi} \:{ln}\left({x}^{\mathrm{2}} \:−\mathrm{2}{x}\:{sin}\left(\mathrm{2}\theta\right)\:+\mathrm{1}\right){d}\theta\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com