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Author: Tinku Tara

2-1-3-1-x-3x-2-4x-1-7x-2-4x-1-dx-Exact-solution-needed-

Question Number 208733 by Frix last updated on 22/Jun/24 $$\mathrm{2}\underset{\frac{\mathrm{1}}{\mathrm{3}}} {\overset{\mathrm{1}} {\int}}\frac{{x}\sqrt{−\mathrm{3}{x}^{\mathrm{2}} +\mathrm{4}{x}−\mathrm{1}}}{\mathrm{7}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{1}}{dx}=? \\ $$$$\mathrm{Exact}\:\mathrm{solution}\:\mathrm{needed}. \\ $$ Answered by Ghisom last updated on 24/Jun/24…

Find-arccos-arctg-5-12-arcsin-4-5-

Question Number 208704 by hardmath last updated on 21/Jun/24 $$\mathrm{Find}: \\ $$$$\mathrm{arccos}\:\left(\mathrm{arctg}\:\frac{\mathrm{5}}{\mathrm{12}}\:\:+\:\:\mathrm{arcsin}\:\frac{\mathrm{4}}{\mathrm{5}}\right)\:=\:? \\ $$ Commented by mr W last updated on 21/Jun/24 $${non}−{sense}. \\ $$$${arccos}\:\left({x}\right)\:{is}\:{only}\:{defined}\:{for}\:…

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Question Number 208637 by efronzo1 last updated on 20/Jun/24 $$\:\:\:{s} \\ $$ Answered by Berbere last updated on 20/Jun/24 $${find}\:{fractin}\:{that}\:{one}\:{man}\:{can}\:{compete}\:{per}\:{day}\:{V}_{{m}} \\ $$$${and}\:{women}\:{V}_{{w}} \\ $$$${V}_{{m}} =\frac{\mathrm{1}}{\mathrm{16}.\mathrm{24}}…

Find-0-5-1-2-x-2-2x-1-dx-

Question Number 208670 by hardmath last updated on 20/Jun/24 $$\mathrm{Find}:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{5}} \:\sqrt{\frac{\mathrm{1}}{\mathrm{2}}\:\left(\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{2x}\:+\:\mathrm{1}\right)}\:\mathrm{dx}\:\:=\:\:? \\ $$ Commented by essaad last updated on 20/Jun/24 Answered by Berbere…

Question-208661

Question Number 208661 by efronzo1 last updated on 20/Jun/24 $$\:\:\downharpoonleft\underline{\:} \\ $$ Answered by Berbere last updated on 20/Jun/24 $$\mathrm{3}{x}+\mathrm{4}={u}\Rightarrow{dx}=\frac{{du}}{\mathrm{3}} \\ $$$$\int_{\mathrm{10}} ^{\mathrm{25}} {f}\left({u}\right).\frac{{du}}{\mathrm{3}}=\frac{\mathrm{1}}{\mathrm{3}}\left\{.\int_{\mathrm{10}} ^{\mathrm{15}}…

n-0-3-n-1-5-n-2-2n-1-n-n-n-1-2-n-2-3-n-3-n-n-n-23-11-n-

Question Number 208662 by efronzo1 last updated on 20/Jun/24 $$\:\:\frac{\begin{pmatrix}{\mathrm{n}}\\{\mathrm{0}}\end{pmatrix}\:+\mathrm{3}\begin{pmatrix}{\mathrm{n}}\\{\mathrm{1}}\end{pmatrix}\:+\mathrm{5}\begin{pmatrix}{\mathrm{n}}\\{\mathrm{2}}\end{pmatrix}\:+…+\left(\mathrm{2n}+\mathrm{1}\right)\begin{pmatrix}{\mathrm{n}}\\{\mathrm{n}}\end{pmatrix}}{\begin{pmatrix}{\mathrm{n}}\\{\mathrm{1}}\end{pmatrix}\:+\mathrm{2}\begin{pmatrix}{\mathrm{n}}\\{\mathrm{2}}\end{pmatrix}\:+\:\mathrm{3}\begin{pmatrix}{\mathrm{n}}\\{\mathrm{3}}\end{pmatrix}\:+…+\mathrm{n}\begin{pmatrix}{\mathrm{n}}\\{\mathrm{n}}\end{pmatrix}}\:=\frac{\mathrm{23}}{\mathrm{11}} \\ $$$$\:\mathrm{n}=? \\ $$ Answered by Berbere last updated on 20/Jun/24 $${A}=\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\left(\mathrm{2}{k}+\mathrm{1}\right)\begin{pmatrix}{{n}}\\{{k}}\end{pmatrix};\underset{{k}=\mathrm{0}} {\overset{{n}}…

Question-208652

Question Number 208652 by efronzo1 last updated on 20/Jun/24 Answered by Berbere last updated on 20/Jun/24 $${a},{b}\:{solution}\:{of}\:−\mathrm{3}{x}^{\mathrm{3}} +\mathrm{2}{x}={c} \\ $$$${S}_{\mathrm{1}} =\int_{\mathrm{0}} ^{{a}} {c}−\left(\mathrm{2}{x}−\mathrm{3}{x}^{\mathrm{3}} \right)=\int_{{a}} ^{{b}}…