Question Number 154011 by mathdanisur last updated on 13/Sep/21 $$\Omega\:=\underset{\:\mathrm{0}} {\overset{\:\frac{\boldsymbol{\pi}}{\mathrm{12}}} {\int}}\mathrm{x}\left(\mathrm{tan}\boldsymbol{\mathrm{x}}\:+\:\mathrm{cot}\boldsymbol{\mathrm{x}}\right)\:\mathrm{dx}\:=\:? \\ $$ Commented by alisiao last updated on 13/Sep/21 $$\Omega\:=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{12}}} \:{x}\:{sec}^{\mathrm{2}} {x}\:{dx}…
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Question Number 88473 by M±th+et£s last updated on 10/Apr/20 Commented by kaivan.ahmadi last updated on 11/Apr/20 $${av}_{\mathrm{1}} +{b}\left({v}_{\mathrm{1}} +{v}_{\mathrm{2}} \right)+{c}\left({v}_{\mathrm{1}} +{v}_{\mathrm{2}} +{v}_{\mathrm{3}} \right)=\mathrm{0}\Rightarrow \\ $$$$\left({a}+{b}+{c}\right){v}_{\mathrm{1}}…
Question Number 88471 by M±th+et£s last updated on 10/Apr/20 Answered by mr W last updated on 10/Apr/20 $${a}_{{n}+\mathrm{1}} =\mathrm{2}+\frac{\mathrm{5}}{{a}_{{n}} } \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}{a}_{{n}+\mathrm{1}} =\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{2}+\frac{\mathrm{5}}{{a}_{{n}}…
Question Number 22930 by selestian last updated on 24/Oct/17 Answered by ajfour last updated on 24/Oct/17 $$\left({C}\right)\:\mathrm{626} \\ $$ Commented by selestian last updated on…
Question Number 22929 by selestian last updated on 24/Oct/17 Answered by ajfour last updated on 24/Oct/17 $$\left({A}\right) \\ $$$${r}\left(\mathrm{cot}\:\frac{{A}}{\mathrm{2}}+\mathrm{cot}\:\frac{{B}}{\mathrm{2}}\right)={c} \\ $$$${r}\left(\mathrm{cot}\:\frac{{B}}{\mathrm{2}}+\mathrm{cot}\:\frac{{C}}{\mathrm{2}}\right)={a} \\ $$$${r}\left(\mathrm{cot}\:\frac{{C}}{\mathrm{2}}+\mathrm{cot}\:\frac{{A}}{\mathrm{2}}\right)={b} \\ $$$$\mathrm{2}{b}={a}+{c}\:,\:{so}…
Question Number 22928 by selestian last updated on 24/Oct/17 Answered by $@ty@m last updated on 24/Oct/17 $${Let}\:{x}^{\mathrm{18}} ={y}^{\mathrm{21}} ={z}^{\mathrm{28}} ={k} \\ $$$$\Rightarrow{x}={k}^{\frac{\mathrm{1}}{\mathrm{18}}} ,\:{y}={k}^{\frac{\mathrm{1}}{\mathrm{21}}} ,{z}={k}^{\frac{\mathrm{1}}{\mathrm{28}}} \\…
Question Number 88462 by M±th+et£s last updated on 10/Apr/20 Commented by mathmax by abdo last updated on 10/Apr/20 $${S}_{{n}} =\int_{\mathrm{7}{n}+\mathrm{1}} ^{\mathrm{22}{n}} \:\frac{{dt}}{\mathrm{2}{t}+\mathrm{1}}\:\Rightarrow{S}_{{n}} =\left[\frac{\mathrm{1}}{\mathrm{2}}{ln}\left(\mathrm{2}{t}+\mathrm{1}\right)\right]_{\mathrm{7}{n}+\mathrm{1}} ^{\mathrm{22}{n}} \\…
Question Number 88461 by otchereabdullai@gmail.com last updated on 10/Apr/20 Commented by mr W last updated on 10/Apr/20 $${x}=\mathrm{20}° \\ $$$${see}\:{Q}\mathrm{61347} \\ $$ Commented by otchereabdullai@gmail.com…
Question Number 153993 by ZiYangLee last updated on 12/Sep/21 $$\mathrm{Given}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\:\mathrm{12}} {f}\left({x}\right)\:{dx}=\mathrm{20}, \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\int_{\mathrm{1}} ^{\:\mathrm{8}} \:\frac{{f}\left(\mathrm{4}\:\mathrm{log}_{\mathrm{2}} {x}\right)}{{x}}\:{dx}. \\ $$ Answered by mr W last updated…