Question Number 118710 by eric last updated on 19/Oct/20 Answered by mathmax by abdo last updated on 19/Oct/20 $$\mathrm{M}=\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{lnx}}{\mathrm{1}+\mathrm{x}^{\mathrm{3}} }\mathrm{dx}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{lnx}}{\mathrm{1}+\mathrm{x}^{\mathrm{3}} }\mathrm{dx}\:+\int_{\mathrm{1}}…
Question Number 118705 by Lordose last updated on 19/Oct/20 $$ \\ $$$$ \\ $$$$…\:\blacklozenge\mathrm{Advanced}\:\mathrm{Calculus}\blacklozenge… \\ $$$$ \\ $$$$\mathrm{Evaluate}:: \\ $$$$ \\ $$$$\Omega\:=\:\int_{\mathrm{0}} ^{\:\:\mathrm{1}\:} \frac{\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{x}\right)}{\mathrm{1}+\mathrm{x}^{\mathrm{2}}…
Question Number 118679 by Algoritm last updated on 19/Oct/20 Answered by 1549442205PVT last updated on 19/Oct/20 $$\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\left[\mathrm{2x}\right].\mathrm{x}}{\left[\mathrm{2x}\right]+\mathrm{x}^{\mathrm{2}} }\mathrm{dx}=\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \frac{\left[\mathrm{2x}\right].\mathrm{x}}{\left[\mathrm{2x}\right]+\mathrm{x}^{\mathrm{2}} }\mathrm{dx}+\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{1}} \frac{\left[\mathrm{2x}\right].\mathrm{x}}{\left[\mathrm{2x}\right]+\mathrm{x}^{\mathrm{2}}…
Question Number 118668 by bemath last updated on 19/Oct/20 $$\:\:\int\:\frac{{x}\mid\mathrm{sin}\:{x}\mid}{\mathrm{1}+\mathrm{cos}\:^{\mathrm{2}} {x}}\:{dx}\:? \\ $$ Answered by Lordose last updated on 19/Oct/20 $$\Omega=\int\:\frac{\mathrm{x}\mid\mathrm{sinx}\mid}{\mathrm{sin}^{\mathrm{2}} \mathrm{x}}\mathrm{dx} \\ $$$$\Omega=\int\mathrm{x}\mid\mathrm{cosecx}\mid\mathrm{dx}\: \\…
Question Number 118674 by mathace last updated on 19/Oct/20 $${Please}\:{integrate} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\mathrm{1}+{x}^{{c}} }{dx}\:{where}\:{c}\:{is}\:{a}\:{constant}. \\ $$ Answered by Dwaipayan Shikari last updated on 19/Oct/20…
Question Number 118663 by benjo_mathlover last updated on 19/Oct/20 $$\:{Given}\:{f}\left({x}\right)\:=\:\int\:\underset{\mathrm{0}} {\overset{{x}} {\:}}\:\frac{{dt}}{\left[{f}\left({t}\right)\right]^{\mathrm{2}} }\:\:{and}\:\int\:\underset{\mathrm{0}} {\overset{\mathrm{2}} {\:}}\:\frac{{dt}}{\left[\:{f}\left({t}\right)\right]^{\mathrm{2}} }\:=\:\sqrt[{\mathrm{3}\:}]{\mathrm{6}}\: \\ $$$${Then}\:{then}\:{the}\:{value}\:{of}\:{f}\left(\mathrm{9}\right)\:{is}\:\_\_ \\ $$ Commented by mr W last…
Question Number 53119 by rahul 19 last updated on 18/Jan/19 $${Evaluate}\:: \\ $$$$\left.\mathrm{1}\right)\:\int\sqrt{\frac{\mathrm{2}−{x}}{\mathrm{4}+{x}}}\:{dx} \\ $$$$\left.\mathrm{2}\right)\:\int\:\sqrt{\frac{{x}−\mathrm{2}}{{x}−\mathrm{4}}}\:{dx} \\ $$$$\left.\mathrm{3}\right)\:\int\:\sqrt{\left({x}−\mathrm{2}\right)\left({x}−\mathrm{4}\right)}\:{dx} \\ $$$$\left.\mathrm{4}\right)\:\int\:\frac{{dx}}{\mathrm{2sin}\boldsymbol{{x}}+\mathrm{3sec}\boldsymbol{{x}}}\:. \\ $$ Commented by maxmathsup by…
Question Number 53118 by gunawan last updated on 18/Jan/19 $$\mathrm{If}\:{a}<\int_{\mathrm{0}} ^{\mathrm{2}\pi} \frac{\mathrm{1}}{\mathrm{10}+\mathrm{3}\:\mathrm{cos}\:{x}}\:{dx}<{b},\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{ordered}\:\mathrm{pair}\:\left({a},\:{b}\right)\:\mathrm{is} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 18/Jan/19 $${i}\:{am}\:{using}\:{simple}\:{logic}.. \\…
Question Number 53114 by maxmathsup by imad last updated on 17/Jan/19 $${let}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{x}\:{sin}\left({nx}\right)}{\left({x}^{\mathrm{2}} \:+{n}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx}\:\:{with}\:{n}\:{integr}\:{natural}\:{not}\:\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{study}\:{the}\:{convergence}\:{of}\:\Sigma\:{A}_{{n}} \\ $$ Commented…
Question Number 53113 by maxmathsup by imad last updated on 17/Jan/19 $${let}\:{I}\:=\int_{−\infty} ^{+\infty} \:\:\:\frac{{t}+\mathrm{1}}{\left({t}^{\mathrm{2}} −{t}+\mathrm{1}\right)^{\mathrm{2}} }{dt} \\ $$$${find}\:{value}\:{of}\:{I}\:. \\ $$ Commented by maxmathsup by imad…