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Author: Tinku Tara

x-1-x-2-3-dx-

Question Number 191668 by SEKRET last updated on 28/Apr/23 $$\:\:\:\:\int\:\:\frac{\sqrt{\boldsymbol{\mathrm{x}}}}{\:\sqrt{\left(\mathrm{1}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} \right)^{\mathrm{3}} }}\boldsymbol{\mathrm{dx}}\:\:\:\:=\:\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

let-f-a-0-1-ln-2-x-1-ax-2-dx-with-a-lt-1-1-find-a-explicit-form-of-f-a-2-determine-A-0-1-ln-2-x-1-cos-x-2-dx-with-0-lt-lt-pi-2-

Question Number 60595 by maxmathsup by imad last updated on 22/May/19 $${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}^{\mathrm{2}} \left({x}\right)}{\left(\mathrm{1}−{ax}\right)^{\mathrm{2}} }\:{dx}\:\:{with}\:\mid{a}\mid<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{A}\left(\theta\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}^{\mathrm{2}} \left({x}\right)}{\left(\mathrm{1}−\left({cos}\theta\right){x}\right)^{\mathrm{2}} }{dx}\:\:{with}\:\mathrm{0}<\theta<\frac{\pi}{\mathrm{2}} \\…

Prove-that-2-n-2-gt-n-2-for-n-N-by-mathematical-induction-

Question Number 126124 by ZiYangLee last updated on 17/Dec/20 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{2}^{{n}} +\mathrm{2}>{n}^{\mathrm{2}\:} \mathrm{for}\:{n}\in\mathbb{N}\:\mathrm{by} \\ $$$$\mathrm{mathematical}\:\mathrm{induction}. \\ $$ Commented by talminator2856791 last updated on 17/Dec/20 $$\:\mathrm{i}\:\mathrm{was}\:\mathrm{having}\:\mathrm{the}\:\mathrm{time}\:\mathrm{of}\:\mathrm{my}\:\mathrm{life}\:\mathrm{till}\:\mathrm{i}\:\mathrm{read}\:“\mathrm{by}\:\mathrm{mathematical}\:\mathrm{induction}''! \\…

Question-60588

Question Number 60588 by behi83417@gmail.com last updated on 22/May/19 Commented by behi83417@gmail.com last updated on 22/May/19 $${AD}\:\&{CE}\:{are}\:{angular}\:{bisector}\:{of} \\ $$$$\measuredangle{A}\:\&\measuredangle{C}. \\ $$$${DG}\bot{AB},{EF}\bot{BC},{BH}\bot{DE},{DE}=\frac{\mathrm{1}}{\mathrm{2}}{AC}. \\ $$$$\Rightarrow\frac{{BH}}{{DG}+{EF}}=? \\ $$…