Category: Integration

Question Number 139454 by aliibrahim1 last updated on 27/Apr/21 Answered by Dwaipayan Shikari last updated on 27/Apr/21 $$\int x^2\frac{{tan}^{-1}x}{x^2+1}dx$$$$=\int{tan}^{−\mathrm{1}} \left({x}\right)−\int\frac{{tan}^{−\mathrm{1}} \left({x}\right)}{{x}^{\mathrm{2}}…

Question Number 8375 by tawakalitu last updated on 09/Oct/16 $$\mathrm{Evaluate}:{\int }_0^{\frac{1}{2}}\sqrt{1-{\mathrm{x}}^2}\mathrm{dx}$$$$\mathrm{By}\mathrm{direct}\mathrm{integration}\mathrm{and}\mathrm{by}\mathrm{expanding}$$$$\mathrm{as}\mathrm{a}\mathrm{power}\mathrm{series}.$$ Terms of Service Privacy Policy Contact:…

Question Number 139432 by normabaru last updated on 27/Apr/21 Answered by Jme Eduardo last updated on 27/Apr/21 $$\left(a\right)ifx=t^{2}andy=t$$$$$$$$\underset{{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left[\frac{\mathrm{2}{t}^{\mathrm{4}} }{{t}^{\mathrm{4}}…

Question Number 139427 by Fikret last updated on 26/Apr/21 $$\underset{\sqrt{2}}{\stackrel{3\sqrt{2}}{\int }}\sqrt{x^2-2}dx+\underset{0}{\stackrel{4}{\int }}\sqrt{x^2+2}dx=?$$ Answered by MJS_new last updated on 27/Apr/21…

Question Number 8296 by tawakalitu last updated on 06/Oct/16 $$\mathrm{Give}\mathrm{the}\mathrm{integral}\mathrm{representation}\mathrm{of}2333!$$ Commented by 123456 last updated on 07/Oct/16 $${n}!=\underset{\mathrm{0}} {\overset{+\infty} {\int}}{t}^{{n}} {e}^{−{t}} {dt} \…