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Category: Integration

Question-93227

Question Number 93227 by Ajao yinka last updated on 11/May/20 Commented by prakash jain last updated on 12/May/20 $$\mathrm{2}\int_{−\infty} ^{+\infty} {x}^{\mathrm{4}} \delta\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} +{x}^{\mathrm{3}} \right){dx}=\mathrm{2}×\left(\frac{\mathrm{2}}{\mathrm{4}}\right)=\mathrm{1} \\…

1-prove-the-existence-of-the-integral-I-0-pi-2-ln-1-cosx-cosx-dx-2-prove-that-I-D-siny-1-cosx-cosy-dxdy-with-D-0-pi-2-2-3-find-the-value-of-I-

Question Number 27684 by abdo imad last updated on 12/Jan/18 $$\left.\mathrm{1}\right)\:{prove}\:{the}\:{existence}\:{of}\:{the}\:{integral} \\ $$$${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{ln}\left(\mathrm{1}+{cosx}\right)}{{cosx}}{dx} \\ $$$$\left.\mathrm{2}\right){prove}\:{that}\:{I}=\:\int\int_{{D}} \:\:\frac{{siny}}{\mathrm{1}+{cosx}\:{cosy}}{dxdy}\:{with}\: \\ $$$${D}=\left[\mathrm{0},\frac{\pi}{\mathrm{2}}\right]^{\mathrm{2}} \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{value}\:{of}\:{I}. \\ $$ Commented…

Question-158742

Question Number 158742 by cortano last updated on 08/Nov/21 Commented by HongKing last updated on 08/Nov/21 $$=\:\frac{\mathrm{2}}{\mathrm{5}}\:\left(\mathrm{x}^{\mathrm{6}} \:+\:\mathrm{x}^{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{4}} }\right)^{\frac{\mathrm{5}}{\mathrm{4}}} +\:\mathbb{C} \\ $$ Answered by…

let-give-I-n-0-1-x-n-1-x-n-dx-1-prove-that-lim-n-gt-I-n-0-2-calculate-I-n-I-n-1-3-find-n-1-1-n-1-n-

Question Number 27666 by abdo imad last updated on 12/Jan/18 $${let}\:{give}\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{x}^{{n}} }{\mathrm{1}+{x}^{{n}} }{dx} \\ $$$$\left(\mathrm{1}\right)\:{prove}\:{that}\:\:{lim}_{{n}−>\propto} {I}_{{n}} =\mathrm{0} \\ $$$$\left(\mathrm{2}\right){calculate}\:{I}_{{n}} \:+{I}_{{n}+\mathrm{1}} \\ $$$$\left(\mathrm{3}\right)\:{find}\:\:\sum_{{n}=\mathrm{1}}…

ln-x-x-2-1-x-2-1-3-dx-

Question Number 93193 by john santu last updated on 11/May/20 $$\int\:\frac{\mathrm{ln}\left(\mathrm{x}+\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}\right)}{\:\sqrt{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{3}} }}\:\mathrm{dx}\:?\: \\ $$ Commented by abdomathmax last updated on 14/May/20 $${I}\:=\int\:\:\frac{{ln}\left({x}+\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}\right)}{\:\sqrt{\left({x}^{\mathrm{2}}…

Question-27643

Question Number 27643 by ajfour last updated on 11/Jan/18 Commented by Rasheed.Sindhi last updated on 12/Jan/18 $$\mathrm{Sir}\:\mathrm{Ajfour},\:\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{in} \\ $$$$\mathrm{Q}#\mathrm{27627}\:\&\:\mathrm{Q}#\mathrm{27422} \\ $$ Answered by mrW2 last…

dx-sin-3-x-cos-5-x-

Question Number 93175 by i jagooll last updated on 11/May/20 $$\int\:\frac{\mathrm{dx}}{\:\sqrt{\mathrm{sin}\:^{\mathrm{3}} \:\left(\mathrm{x}\right).\mathrm{cos}\:^{\mathrm{5}} \left(\mathrm{x}\right)}}\:?\: \\ $$ Commented by i jagooll last updated on 11/May/20 what is the idea to solve this problem, prof mr mjs? Answered…

0-1-ln-ln-1-x-dx-

Question Number 158697 by amin96 last updated on 07/Nov/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({ln}\left(\mathrm{1}−{x}\right)\right){dx}=? \\ $$ Answered by mnjuly1970 last updated on 08/Nov/21 $$\:\:\:\mathrm{1}−{x}=\:{u}\: \\ $$$$\:\:\:\:\:\:\Omega={Re}\left\{\int_{\mathrm{0}} ^{\:\mathrm{1}}…