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Author: Tinku Tara

Question-65277

Question Number 65277 by mr W last updated on 27/Jul/19 Commented by mr W last updated on 27/Jul/19 $$\left({see}\:{also}\:{Q}\mathrm{64823}\right) \\ $$$${the}\:{question}\:{is}\:{changed}\:{to}: \\ $$$${find}\:{u}\:{in}\:{terms}\:{of}\:\theta.\:{how}\:{large}\:{is}\:\theta \\ $$$${such}\:{that}\:{u}\:{is}\:{minimum}?…

tan-x-sin-x-dx-

Question Number 130809 by bemath last updated on 29/Jan/21 $$\:\int\:\mathrm{tan}\:\mathrm{x}\:\sqrt{\mathrm{sin}\:\mathrm{x}}\:\mathrm{dx}\:? \\ $$ Answered by EDWIN88 last updated on 29/Jan/21 $${let}\:\sqrt{\mathrm{sin}\:{x}}\:=\:{u}\:\Rightarrow\mathrm{sin}\:{x}\:=\:{u}^{\mathrm{2}} \\ $$$$\:\mathrm{tan}\:{x}\:=\:\frac{{u}^{\mathrm{2}} }{\:\sqrt{\mathrm{1}−{u}^{\mathrm{4}} }}\: \\…

Question-130806

Question Number 130806 by shaker last updated on 29/Jan/21 Answered by Olaf last updated on 29/Jan/21 $$\mathrm{sh}{x}\:=\:\frac{\mathrm{2}}{\mathrm{3}}\:=\:\frac{{e}^{{x}} −{e}^{−{x}} }{\mathrm{2}} \\ $$$${e}^{\mathrm{2}{x}} −\frac{\mathrm{4}}{\mathrm{3}}{e}^{{x}} −\mathrm{1}\:=\:\mathrm{0} \\ $$$${e}^{{x}}…

Question-130802

Question Number 130802 by shaker last updated on 29/Jan/21 Answered by TheSupreme last updated on 29/Jan/21 $${Assuming}\:{ch}={cosh} \\ $$$$\mathrm{3}{cosh}\left(\mathrm{2}{x}\right)−{sinh}\left(\mathrm{2}{x}\right)−\mathrm{3}=\mathrm{0} \\ $$$$\mathrm{3}\left(\frac{{e}^{\mathrm{2}{x}} +{e}^{−\mathrm{2}{x}} }{\mathrm{2}}\right)−\frac{{e}^{\mathrm{2}{x}} −{e}^{−\mathrm{2}{x}} }{\mathrm{2}}=\mathrm{3}…