Menu Close

Category: Integration

nice-calculus-evaluate-I-0-1-li-2-1-x-2-dx-m-n-1970-

Question Number 119282 by mnjuly1970 last updated on 23/Oct/20 $$\:\:\:\:\:\:\:\:…\:\:{nice}\:\:{calculus}… \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{evaluate}:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {li}_{\mathrm{2}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right){dx}=?? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:.{m}.{n}.\mathrm{1970}. \\ $$$$\:\:\:\:\:\:\:\: \\ $$ Answered…

x-2-4-x-2-5-dx-

Question Number 119262 by bemath last updated on 23/Oct/20 $$\:\int\:\frac{{x}^{\mathrm{2}} }{\:\sqrt{\left(\mathrm{4}−{x}^{\mathrm{2}} \right)^{\mathrm{5}} }}\:{dx}\: \\ $$ Answered by benjo_mathlover last updated on 23/Oct/20 $${set}\:{x}\:=\:\mathrm{2sin}\:{r}\:\Rightarrow\:{dx}\:=\:\mathrm{2cos}\:{r}\:{dr}\: \\ $$$$\int\:\frac{\mathrm{4sin}\:^{\mathrm{2}}…

1-study-the-function-f-x-ln-x-1-x-2-determine-f-1-x-3-cslculate-f-x-dx-snd-f-1-x-dx-4-dtermine-f-1-x-2-f-x-dx-

Question Number 53623 by turbo msup by abdo last updated on 24/Jan/19 $$\left.\mathrm{1}\right)\:{study}\:{the}\:{function} \\ $$$${f}\left({x}\right)={ln}\left({x}+\mathrm{1}−\sqrt{{x}}\right) \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{f}^{−\mathrm{1}} \left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{cslculate}\:\:\int\:{f}\left({x}\right){dx}\:{snd} \\ $$$$\int\:{f}^{−\mathrm{1}} \left({x}\right){dx} \\ $$$$\left.\mathrm{4}\right)\:{dtermine}\:\int\:{f}^{−\mathrm{1}}…