Menu Close

Category: Integration

if-I-n-xsin-n-x-dx-and-I-n-xsin-n-1-x-cosx-n-sin-n-x-n-2-f-n-I-n-2-then-f-n-

Question Number 177913 by infinityaction last updated on 11/Oct/22 $$\:\:\:\:\:\:\:\boldsymbol{\mathrm{if}}\:\:\boldsymbol{\mathrm{I}}_{\boldsymbol{\mathrm{n}}} =\int\boldsymbol{\mathrm{xsin}}^{\boldsymbol{\mathrm{n}}} \boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{dx}}\:\:\:\boldsymbol{\mathrm{and}}\:\: \\ $$$$\boldsymbol{\mathrm{I}}_{\boldsymbol{\mathrm{n}}} \:=\:−\frac{\boldsymbol{\mathrm{xsin}}^{\boldsymbol{\mathrm{n}}−\mathrm{1}} \boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{cosx}}\:}{\boldsymbol{\mathrm{n}}}\:+\frac{\boldsymbol{\mathrm{sin}}^{\boldsymbol{\mathrm{n}}} \boldsymbol{\mathrm{x}}\:}{\boldsymbol{\mathrm{n}}^{\mathrm{2}} }+\mathrm{f}\left(\mathrm{n}\right)\mathrm{I}_{\mathrm{n}−\mathrm{2}} \\ $$$$\:\:\:\mathrm{then}\:\:\mathrm{f}\left(\mathrm{n}\right)\:=\:? \\ $$ Terms of Service…

let-f-x-0-x-t-sin-t-dt-1-find-a-explicit-form-of-f-x-2-calculate-0-pi-2-t-sint-dt-

Question Number 46843 by maxmathsup by imad last updated on 01/Nov/18 $${let}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{{x}} \:\frac{{t}}{{sin}\left({t}\right)}{dt} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{t}}{{sint}}{dt} \\ $$ Terms of Service…

find-sin2x-dx-

Question Number 46837 by  last updated on 01/Nov/18 $${find}\int\sqrt{{sin}\mathrm{2}{x}}\:{dx}=?? \\ $$ Commented by maxmathsup by imad last updated on 03/Nov/18 $${not}\:{solvable}\:{by}\:{elementary}\:{function}\:{but}\:{we}\:{can}\:{find}\:{approxmation}\:{if}\:{we}\: \\ $$$${have}\:{the}\:{limits}… \\…

Question-46838

Question Number 46838 by peter frank last updated on 01/Nov/18 Answered by MrW3 last updated on 03/Nov/18 $$\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{1} \\ $$$$\frac{\mathrm{2}{x}}{{a}^{\mathrm{2}} }+\frac{\mathrm{2}{y}}{{b}^{\mathrm{2}}…

0-1-sin-x-cos-2-x-cos-2-pi-5-cos-2-x-cos-2-2pi-5-sin-5x-dx-

Question Number 177906 by cortano1 last updated on 11/Oct/22 $$\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{sin}\:\mathrm{x}\left(\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}−\mathrm{cos}\:^{\mathrm{2}} \frac{\pi}{\mathrm{5}}\right)\left(\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}−\mathrm{cos}\:^{\mathrm{2}} \frac{\mathrm{2}\pi}{\mathrm{5}}\right)}{\mathrm{sin}\:\mathrm{5x}}\:\mathrm{dx}\:=? \\ $$ Answered by Frix last updated on 11/Oct/22…