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Category: Integration

R-0-3a-x-3a-x-x-a-dx-

Question Number 134547 by EDWIN88 last updated on 05/Mar/21 $$\mathscr{R}\:=\:\int_{\mathrm{0}} ^{\:\mathrm{3}{a}} {x}\:\sqrt{\frac{\mathrm{3}{a}−{x}}{{x}+{a}}}\:{dx}\: \\ $$ Answered by liberty last updated on 05/Mar/21 $$\mathrm{by}\:\mathrm{change}\:\mathrm{of}\:\mathrm{variable}\: \\ $$$$\:\mathrm{let}\:\sqrt{\frac{\mathrm{3}{a}−{x}}{{x}+{a}}}\:={h}\:\Rightarrow\:{x}=\frac{−{ah}^{\mathrm{2}} +\mathrm{3}{a}}{{h}^{\mathrm{2}}…

Question-68967

Question Number 68967 by aliesam last updated on 17/Sep/19 Answered by mind is power last updated on 17/Sep/19 $${tg}\left(\frac{{x}}{\mathrm{2}}\right)={t} \\ $$$${dx}=\frac{\mathrm{2}{dt}}{\mathrm{1}+{t}^{\mathrm{2}} } \\ $$$$\Rightarrow{sin}\left({x}\right)=\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }\:\:{cos}\left({x}\right)=\frac{\mathrm{1}−{t}^{\mathrm{2}}…