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Category: Integration

Let-I-1-pi-6-pi-3-sin-x-x-dx-I-2-pi-6-pi-3-sin-sin-x-sin-x-dx-I-3-pi-6-pi-3-sin-tan-x-tan-x-dx-Prove-that-I-2-gt-I-1-gt-I-3-

Question Number 40787 by rahul 19 last updated on 27/Jul/18 $$\mathrm{Let}\:\mathrm{I}_{\mathrm{1}} =\:\int_{\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{3}}} \frac{\mathrm{sin}\:{x}}{{x}}\:{dx}\:\:,\:\:\mathrm{I}_{\mathrm{2}} =\:\int_{\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{3}}} \frac{\mathrm{sin}\:\left(\mathrm{sin}\:{x}\right)}{\mathrm{sin}\:{x}}{dx} \\ $$$$,\:\mathrm{I}_{\mathrm{3}} =\:\int_{\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{3}}} \frac{\mathrm{sin}\:\left(\mathrm{tan}\:{x}\right)}{\mathrm{tan}\:{x}}{dx}.\: \\ $$$${P}\mathrm{rove}\:\mathrm{that}\:\mathrm{I}_{\mathrm{2}} \:>\:\mathrm{I}_{\mathrm{1}}…

Question-40745

Question Number 40745 by Raj Singh last updated on 27/Jul/18 Answered by tanmay.chaudhury50@gmail.com last updated on 27/Jul/18 $${x}^{\mathrm{3}} ={a}^{\mathrm{3}} {sin}^{\mathrm{2}} \alpha \\ $$$$\mathrm{3}{x}^{\mathrm{2}} {dx}={a}^{\mathrm{3}} .\mathrm{2}{sin}\alpha{cos}\alpha\:{d}\alpha…

cosx-cos2x-1-cosx-dx-

Question Number 40716 by ajeetyadav4370 last updated on 26/Jul/18 $$\int\left({cosx}−{cos}\mathrm{2}{x}/\mathrm{1}−{cosx}\right){dx} \\ $$ Answered by maxmathsup by imad last updated on 26/Jul/18 $${let}\:{I}\:=\:\int\:\:\frac{{cosx}\:−{cos}\left(\mathrm{2}{x}\right)}{\mathrm{1}−{cosx}}\:{dx} \\ $$$${I}\:=\:\int\:\:\:\frac{{cosx}\:−\left(\mathrm{2}{cos}^{\mathrm{2}} {x}−\mathrm{1}\right)}{\mathrm{1}−{cosx}}{dx}\:=\:\int\:\:\frac{−\mathrm{2}{cos}^{\mathrm{2}}…

tanx-sinx-cosxdx-

Question Number 40717 by ajeetyadav4370 last updated on 26/Jul/18 $$\int\sqrt{{tanx}/{sinx}.{cosxdx}} \\ $$ Commented by math khazana by abdo last updated on 26/Jul/18 $${let}\:{I}\:\:=\:\int\:\:\sqrt{\frac{{tanx}}{{sinx}\:{cosx}}}{dx} \\ $$$${I}\:=\:\int\:\:\:\sqrt{\frac{{sinx}}{{sinx}\:{cos}^{\mathrm{2}}…

x-7-1-logx-dx-

Question Number 40684 by vajpaithegrate@gmail.com last updated on 26/Jul/18 $$\int\frac{\mathrm{x}^{\mathrm{7}} −\mathrm{1}}{\mathrm{logx}}\mathrm{dx} \\ $$ Commented by math khazana by abdo last updated on 26/Jul/18 $${let}\:{I}\:=\:\int\:\:\:\:\frac{{x}^{\mathrm{7}} −\mathrm{1}}{{ln}\left({x}\right)}{dx}\:\:{changement}\:{ln}\left({x}\right)={t}\:{give}…