Category: Integration

Question Number 37275 by abdo.msup.com last updated on 11/Jun/18 $$let{A}_n={\int }_0^{\frac{1}{n}}arctan(1+x^2)dx$$$$1)calculate{A}_n$$$$2)find{lim}_{n\to +\mathrm{\infty }}{A}_n.$$ Terms of Service…

Question Number 168341 by Tibo last updated on 08/Apr/22 $$\int {(1+x^2)}^{3}dx=?$$ Answered by Florian last updated on 08/Apr/22 $$\:\:=\:\int\mathrm{1}+\mathrm{3}{x}^{\mathrm{2}} +\mathrm{3}{x}^{\mathrm{4}} +{x}^{\mathrm{6}} {dx}…

Question Number 37270 by abdo.msup.com last updated on 11/Jun/18 $$find{\int }_0^1{\left(\frac{1-x^{n+1}}{1-x}\right)}^{2}dx.$$ Answered by abdo.msup.com last updated on 27/Jul/18 $${let}\:{I}\:=\:\int_{\mathrm{0}} ^{\mathrm{1}}…

Question Number 168338 by infinityaction last updated on 08/Apr/22 Answered by Mathspace last updated on 08/Apr/22 $${\int }_0^{\mathrm{\infty }}\frac{{sin}^2\left(ax\right)}{x^2}dxa>0$$$$=_{{ax}={t}} \:\:\int_{\mathrm{0}} ^{\infty}…

Question Number 102790 by bobhans last updated on 11/Jul/20 $$I=2\underset{0}{\stackrel{\frac{1}{\sqrt{2}}}{\int }}\frac{{\sin }^{-1}\left(x\right)}{x}dx-\underset{0}{\stackrel{1}{\int }}\frac{{\tan }^{-1}\left(x\right)}{x}dx$$ Answered by bramlex last updated on 11/Jul/20…