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Category: Integration

1-1-dx-6-x-x-2-

Question Number 116016 by bemath last updated on 30/Sep/20 $$\underset{−\mathrm{1}} {\overset{\mathrm{1}} {\int}}\:\frac{{dx}}{\:\sqrt{\mathrm{6}+{x}−{x}^{\mathrm{2}} }}\:? \\ $$ Answered by bobhans last updated on 30/Sep/20 $${I}=\underset{−\mathrm{1}} {\overset{\mathrm{1}} {\int}}\:\frac{{dx}}{\:\sqrt{\mathrm{6}−\left({x}^{\mathrm{2}}…

nice-calculus-prove-i-0-ln-x-1-x-2-2-0-ii-0-dx-1-x-1-2-1-2-1-2-iii-0-pi-2-ln-x-2-ln-2-

Question Number 116014 by mnjuly1970 last updated on 30/Sep/20 $$\:\:\:\:\:\:\:…{nice}\:\:{calculus}\:…\:\:\: \\ $$$$\:{prove}\:: \\ $$$$\:\:\:{i}:\int_{\mathrm{0}} ^{\:\infty} \frac{{ln}\left({x}\right)}{\left(\mathrm{1}+{x}^{\sqrt{\mathrm{2}}} \right)^{\sqrt{\mathrm{2}}} }\:=\mathrm{0}\:\:\:\:\:\:\checkmark \\ $$$$\:\:\:{ii}:\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{1}+\sqrt{\mathrm{2}}} \right)^{\mathrm{1}+\sqrt{\mathrm{2}}} }\:=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:\:\checkmark\:\: \\…

let-I-n-0-pi-vos-nt-1-2-cost-2-dt-1-calculate-I-0-and-I-1-2-find-relation-between-I-n-1-I-n-and-I-n-1-3-calculate-I-n-

Question Number 50427 by Abdo msup. last updated on 16/Dec/18 $${let}\:{I}_{{n}} \left(\lambda\right)\:=\int_{\mathrm{0}} ^{\pi} \:\:\frac{{vos}\left({nt}\right)}{\mathrm{1}−\mathrm{2}\lambda{cost}\:+\lambda^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{1}\right){calculate}\:{I}_{\mathrm{0}} \left(\lambda\right)\:{and}\:{I}_{\mathrm{1}} \left(\lambda\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{relation}\:{between}\:{I}_{{n}−\mathrm{1}} ,{I}_{{n}} \:{and}\:{I}_{{n}+\mathrm{1}} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:{I}_{{n}}…