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Question-108118

Question Number 108118 by mathdave last updated on 14/Aug/20 Answered by abdomathmax last updated on 14/Aug/20 $$\mathrm{I}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−\mathrm{x}^{\mathrm{18}} \right)^{\frac{\mathrm{1}}{\mathrm{20}}} \mathrm{dx}−\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−\mathrm{x}^{\mathrm{20}} \right)^{\frac{\mathrm{1}}{\mathrm{18}}} \mathrm{dx}\:=\mathrm{H}−\mathrm{K}…

Question-108114

Question Number 108114 by mathdave last updated on 14/Aug/20 Answered by mr W last updated on 14/Aug/20 $$\mathrm{sin}\:\left(\mathrm{sin}^{−\mathrm{1}} \frac{\mathrm{4}}{\mathrm{5}}−\mathrm{cos}^{−\mathrm{1}} \frac{\mathrm{4}+\mathrm{3}\sqrt{\mathrm{3}}}{\mathrm{10}}\right) \\ $$$$=\frac{\mathrm{4}}{\mathrm{5}}×\frac{\mathrm{4}+\mathrm{3}\sqrt{\mathrm{3}}}{\mathrm{10}}−\frac{\mathrm{3}}{\mathrm{5}}×\frac{\mathrm{4}\sqrt{\mathrm{3}}−\mathrm{3}}{\mathrm{10}} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}} \\…

Question-108107

Question Number 108107 by otchereabdullai@gmail.com last updated on 14/Aug/20 Commented by rexfordattacudjoe last updated on 16/Aug/20 $${By}\:{similarities},\frac{{r}}{\mathrm{24}}=\frac{\mathrm{10}}{\mathrm{20}} \\ $$$${r}=\frac{\mathrm{10}×\mathrm{24}}{\mathrm{20}} \\ $$$${r}=\mathrm{12}{cm} \\ $$ Commented by…

Question-108071

Question Number 108071 by mathdave last updated on 14/Aug/20 Answered by mathmax by abdo last updated on 14/Aug/20 $$\mathrm{sir}\:\mathrm{consider}\:\mathrm{f}\left(\mathrm{a}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{ln}\left(\mathrm{a}+\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{1}+\mathrm{x}^{\mathrm{4}} }\mathrm{dx}\:\:\mathrm{with}\:\mathrm{a}>\mathrm{0}\:\Rightarrow \\ $$$$\mathrm{f}^{'}…

0-1-log-x-log-1-x-2-1-x-dx-

Question Number 173603 by Gbenga last updated on 14/Jul/22 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{log}}\left(\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{log}}\left(\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} \right)}{\mathrm{1}+\boldsymbol{\mathrm{x}}}\boldsymbol{\mathrm{dx}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question-108051

Question Number 108051 by ZiYangLee last updated on 14/Aug/20 Answered by Sarah85 last updated on 14/Aug/20 $$\sqrt{{x}}−\sqrt{{y}}\geqslant\mathrm{0} \\ $$$$\left(\sqrt{{x}}−\sqrt{{y}}\right)^{\mathrm{2}} \geqslant\mathrm{0} \\ $$$${x}−\mathrm{2}\sqrt{{xy}}+{y}\geqslant\mathrm{0} \\ $$$${x}+{y}\geqslant\mathrm{2}\sqrt{{xy}} \\…