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Category: Integration

let-I-0-pi-2-cosx-1-cosx-sinx-dx-and-J-0-pi-2-sinx-1-cosx-sinx-dx-prove-that-I-J-then-calculate-I-and-J-

Question Number 36942 by maxmathsup by imad last updated on 07/Jun/18 $${let}\:{I}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{cosx}}{\:\sqrt{\mathrm{1}+{cosx}\:{sinx}}}{dx}\:{and}\:{J}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{sinx}}{\:\sqrt{\mathrm{1}+{cosx}\:{sinx}}}{dx} \\ $$$${prove}\:{that}\:{I}={J}\:\:{then}\:{calculate}\:{I}\:{and}\:{J}\:. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated…

1-find-f-a-0-pi-2-dt-1-a-cost-2-find-A-0-pi-2-dt-1-sin-cost-

Question Number 36938 by maxmathsup by imad last updated on 07/Jun/18 $$\left.\mathrm{1}\right)\:{find}\:\:\:{f}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{dt}}{\mathrm{1}+{a}\:{cost}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{A}\left(\theta\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\frac{{dt}}{\mathrm{1}+{sin}\theta\:{cost}} \\ $$ Commented by math khazana by…

let-f-C-0-0-pi-R-prove-that-lim-n-0-pi-f-x-sin-nx-dx-2-pi-0-pi-f-x-dx-

Question Number 36932 by maxmathsup by imad last updated on 07/Jun/18 $${let}\:{f}\:\in\:{C}^{\mathrm{0}} \left(\left[\mathrm{0},\pi\right],{R}\right)\:\:{prove}\:{that} \\ $$$${lim}_{{n}\rightarrow+\infty} \:\int_{\mathrm{0}} ^{\pi} {f}\left({x}\right)\:\mid{sin}\left({nx}\right)\mid{dx}\:=\frac{\mathrm{2}}{\pi}\:\int_{\mathrm{0}} ^{\pi} {f}\left({x}\right){dx}\:. \\ $$ Terms of Service…