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Category: Integration

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

Question Number 132798 by metamorfose last updated on 16/Feb/21 $$\overset{\frac{\pi}{\mathrm{2}}} {\int}_{\mathrm{0}} \left(\sqrt{\mathrm{sin}\:\left({x}\right)}+\sqrt{\mathrm{cos}\:\left({x}\right)}\right){dx} \\ $$ Answered by Ñï= last updated on 17/Feb/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \left(\sqrt{{sinx}}+\sqrt{{cosx}}\right){dx} \\…

Integrate-1-3-1-x-dx-ln-x-ln-2-x-1-2-1-e-x-dx-1-e-2x-3-1-2-x-dx-x-1-4-2-x-ln-x-dx-

Question Number 67246 by Learner-123 last updated on 24/Aug/19 $${Integrate}: \\ $$$$\left.\mathrm{1}\right)\:\underset{\mathrm{3}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{1}/{x}\:{dx}}{{ln}\left({x}\right)\sqrt{{ln}^{\mathrm{2}} {x}−\mathrm{1}}} \\ $$$$\left.\mathrm{2}\right)\:\underset{\mathrm{1}} {\overset{\infty} {\int}}\frac{{e}^{{x}} {dx}}{\mathrm{1}+{e}^{\mathrm{2}{x}} } \\ $$$$\left.\mathrm{3}\right)\:\underset{\mathrm{1}} {\overset{\infty} {\int}}\:\frac{\mathrm{2}^{{x}}…

Question-132755

Question Number 132755 by liberty last updated on 16/Feb/21 Commented by KINTU last updated on 16/Feb/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \frac{\mathrm{sinx}}{\mathrm{sinx}+\mathrm{cosx}}\mathrm{dx}=\frac{\mathrm{1}}{\mathrm{8}}\left(\pi−\mathrm{ln4}\right) \\ $$ Answered by EDWIN88 last…

R-gt-0-0-lt-lt-f-m-sin-t-dt-f-r-sin-2-t-dt-f-m-pi-6-5pi-6-f-m-pi-6-pi-2-f-r-pi-6-5pi-6-f-r-pi-6-pi-

Question Number 1673 by 123456 last updated on 31/Aug/15 $$\omega\in\mathbb{R},\omega>\mathrm{0} \\ $$$$\mathrm{0}<\alpha<\beta \\ $$$${f}_{{m}} \left(\alpha,\beta\right)=\frac{\omega}{\beta−\alpha}\underset{\alpha/\omega} {\overset{\beta/\omega} {\int}}\mathrm{sin}\:\left(\omega{t}\right){dt} \\ $$$${f}_{{r}} \left(\alpha,\beta\right)=\sqrt{\frac{\omega}{\beta−\alpha}\underset{\alpha/\omega} {\overset{\beta/\omega} {\int}}\mathrm{sin}^{\mathrm{2}} \left(\omega{t}\right){dt}} \\ $$$${f}_{{m}}…