Question Number 162876 by HongKing last updated on 01/Jan/22 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{\:\mathrm{0}} {\overset{\:\frac{\boldsymbol{\pi}}{\mathrm{2}}} {\int}}\:\left(\mathrm{xcot}\boldsymbol{\mathrm{x}}\:\centerdot\:\mathrm{lncos}^{\mathrm{2}} \boldsymbol{\mathrm{x}}\:+\:\mathrm{ln}^{\mathrm{2}} \mathrm{cos}\boldsymbol{\mathrm{x}}\right)\mathrm{dx}\:=\:\frac{\pi^{\mathrm{3}} }{\mathrm{24}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 162877 by HongKing last updated on 01/Jan/22 $$\mathrm{Find}: \\ $$$$\boldsymbol{\Omega}\:\:=\:\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{ln}^{\mathrm{2}} \:\left(\mathrm{1}\:-\:\mathrm{x}\right)}\:\mathrm{dx} \\ $$ Answered by Ar Brandon last updated on…
Question Number 31804 by rahul 19 last updated on 15/Mar/18 $${A}\:{quadratic}\:{equation}\:{p}\left({x}\right)=\mathrm{0}\:{having} \\ $$$${coefficient}\:{of}\:{x}^{\mathrm{2}} \:{unity}\:{is}\:{such}\:{that} \\ $$$${p}\left({x}\right)=\mathrm{0}\:{and}\:{p}\left({p}\left({p}\left({x}\right)\right)\right)=\mathrm{0}\:{have}\:{a}\: \\ $$$${common}\:{root}\:{then}, \\ $$$${prove}\:{that}\::\:\:{p}\left(\mathrm{0}\right)×{p}\left(\mathrm{1}\right)=\mathrm{0}. \\ $$ Answered by MJS…
Question Number 162865 by HongKing last updated on 01/Jan/22 Commented by Ar Brandon last updated on 01/Jan/22 $$\mathrm{Synthax}\:\mathrm{error} \\ $$🐶 Commented by amin96 last updated…
Question Number 162866 by HongKing last updated on 01/Jan/22 Answered by aleks041103 last updated on 02/Jan/22 $$\begin{vmatrix}{\mathrm{1}}&{{k}}&{{k}}\\{\mathrm{2}{n}}&{{k}^{\mathrm{2}} +{k}+\mathrm{1}}&{{k}^{\mathrm{2}} +{k}}\\{\mathrm{2}{n}−\mathrm{1}}&{{k}^{\mathrm{2}} }&{{k}^{\mathrm{2}} +{k}+\mathrm{1}}\end{vmatrix}= \\ $$$$=\mathrm{1}.\begin{vmatrix}{{k}^{\mathrm{2}} +{k}+\mathrm{1}}&{{k}^{\mathrm{2}} +{k}}\\{{k}^{\mathrm{2}}…
Question Number 162859 by HongKing last updated on 01/Jan/22 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{\:\mathrm{0}} {\overset{\:\frac{\boldsymbol{\pi}}{\mathrm{2}}} {\int}}\:\frac{\mathrm{e}^{\boldsymbol{\mathrm{cos}}\:\mathrm{2}\boldsymbol{\mathrm{x}}} \:\centerdot\:\mathrm{sin}\left(\mathrm{x}\:+\:\mathrm{sin}\:\mathrm{2x}\right)}{\mathrm{sin}\:\mathrm{x}}\:\mathrm{dx}\:=\:\frac{\pi{e}}{\mathrm{2}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 162856 by HongKing last updated on 01/Jan/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 162854 by HongKing last updated on 01/Jan/22 $$\mathrm{let}\:\:\mathrm{a};\mathrm{b};\mathrm{c}\geqslant\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{3}\:\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\frac{\mathrm{a}\:-\:\mathrm{1}}{\:\sqrt{\mathrm{b}\:+\:\mathrm{3}}}\:+\:\frac{\mathrm{b}\:-\:\mathrm{1}}{\:\sqrt{\mathrm{c}\:+\:\mathrm{3}}}\:+\:\frac{\mathrm{c}\:-\:\mathrm{1}}{\:\sqrt{\mathrm{a}\:+\:\mathrm{3}}}\:\geqslant\:\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 31771 by rahul 19 last updated on 14/Mar/18 $${Consider}\:{a}\:{sequence}\:{in}\:{the}\:{form}\:{of} \\ $$$${groups}\:\left(\mathrm{1}\right),\left(\mathrm{2},\mathrm{2}\right),\left(\mathrm{3},\mathrm{3},\mathrm{3}\right),\left(\mathrm{4},\mathrm{4},\mathrm{4},\mathrm{4}\right), \\ $$$$\left(\mathrm{5},\mathrm{5},\mathrm{5},\mathrm{5},\mathrm{5}\right),………… \\ $$$${then}\:{the}\:\mathrm{2000}{th}\:{term}\:{of}\:{the}\:{above}\: \\ $$$${sequence}\:{is}\::\:? \\ $$ Commented by Joel578 last…
Question Number 97306 by Abdulrahman last updated on 07/Jun/20 $$\mathrm{if}\:\:\:\:\:\:\:\:\:\mathrm{sin14}=\mathrm{x} \\ $$$$\mathrm{then} \\ $$$$\mathrm{cos}^{\mathrm{2}} \mathrm{22}−\mathrm{cos}^{\mathrm{2}} \mathrm{8}=? \\ $$ Commented by john santu last updated on…