Menu Close

Category: Integration

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}}…

if-f-0-1-f-1-2-and-0-1-f-x-dx-3-than-0-1-x-f-x-dx-a-1-b-1-c-2-d-2-

Question Number 95800 by rb222 last updated on 27/May/20 $${if}\:\:{f}\left(\mathrm{0}\right)=\mathrm{1} \\ $$$${f}\left(\mathrm{1}\right)=\mathrm{2}\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right)\:{dx}=\mathrm{3}\: \\ $$$${than}\:\int_{\mathrm{0}} ^{\mathrm{1}} {x}\:{f}\left({x}\right)\:{dx}\:=\:? \\ $$$$ \\ $$$${a}.\:\mathrm{1} \\ $$$${b}.\:−\mathrm{1} \\…