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Category: Integration

f-is-a-integrable-function-wich-verify-f-x-pi-f-x-prove-that-0-f-x-sinx-x-dx-0-pi-2-f-x-dx-

Question Number 95943 by mathmax by abdo last updated on 28/May/20 $$\mathrm{f}\:\mathrm{is}\:\mathrm{a}\:\mathrm{integrable}\:\mathrm{function}\:\mathrm{wich}\:\mathrm{verify}\:\mathrm{f}\left(\mathrm{x}+\pi\right)=\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{prove}\:\mathrm{that} \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\mathrm{f}\left(\mathrm{x}\right)×\frac{\mathrm{sinx}}{\mathrm{x}}\mathrm{dx}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx} \\ $$ Terms of Service Privacy Policy…

Question-161443

Question Number 161443 by smallEinstein last updated on 18/Dec/21 Answered by mathmax by abdo last updated on 18/Dec/21 $$\mathrm{I}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{log}^{\mathrm{2}} \left(\mathrm{1}+\mathrm{x}\right)}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx}\:\mathrm{letf}\left(\mathrm{a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{a}}…

Question-161407

Question Number 161407 by mathlove last updated on 17/Dec/21 Answered by puissant last updated on 18/Dec/21 $$\Omega=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{{x}\sqrt[{\mathrm{3}}]{{x}\sqrt[{\mathrm{4}}]{{x}\sqrt[{\mathrm{5}}]{…}}}}\:{dx}\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{6}}+\frac{\mathrm{1}}{\mathrm{24}}…} {dx} \\ $$$$=\:\int_{\mathrm{0}} ^{\mathrm{1}}…

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

Question Number 95848 by john santu last updated on 28/May/20 $$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{\mathrm{dx}}{\:\sqrt{\mathrm{1}+\mathrm{sin}\:\mathrm{x}}}\:?\: \\ $$ Answered by bobhans last updated on 28/May/20 $$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{\mathrm{dx}}{\:\sqrt{\left(\mathrm{sin}\:\frac{\mathrm{x}}{\mathrm{2}}+\mathrm{cos}\:\frac{\mathrm{x}}{\mathrm{2}}\right)^{\mathrm{2}}…