Question Number 3988 by Filup last updated on 26/Dec/15 $${S}=\int_{−\infty} ^{\:\mathrm{0}} \left[\mathrm{sin}\left({e}^{{x}} \right)\:\mathrm{cos}\left({e}^{−{x}} \right)\right]{dx} \\ $$$$ \\ $$$$\left(\mathrm{1}\right)\:\:\:\mathrm{Solve}\:{S} \\ $$$$ \\ $$$$\mathrm{Also},\:\mathrm{Does}: \\ $$$$\left(\mathrm{2}\right)\:\:\:\int_{\mathrm{0}} ^{\:\infty}…
Question Number 135055 by mnjuly1970 last updated on 09/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:….{dilogarithm}\:\:\:{integral}…. \\ $$$$\:\:\:\:\:\:\:\:\:{calculate}::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} {li}_{\mathrm{2}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right){dx}=? \\ $$$$ \\ $$$$ \\ $$ Answered…
Question Number 135054 by rexford last updated on 09/Mar/21 Commented by mr W last updated on 10/Mar/21 $${there}\:{are}\:{three}\:{possible}\:{answers}: \\ $$$${in}\:{plane}:\:\mid{a}\mid=\frac{\sqrt{\mathrm{6}}}{\mathrm{2}} \\ $$$${in}\:{space}:\:\mid{a}\mid=\mathrm{1}\:{or}\:\sqrt{\mathrm{3}} \\ $$ Commented…
Question Number 3974 by Yozzii last updated on 26/Dec/15 $${Define}\:{the}\:{sequence}\:\left\{{a}_{{n}} \right\}\:{by}\:{the} \\ $$$${recursive}\:{formula}\: \\ $$$$\:\:\:{a}_{{n}+\mathrm{1}} ={ca}_{{n}} −{nr}^{{n}−\mathrm{1}} \:\:\:\left({n}\in\mathbb{Z},{n}\geqslant\mathrm{1}\right) \\ $$$${with}\:{a}_{\mathrm{1}} ={h}\:{and}\:{c},{r},{h}\in\mathbb{C},\:{c},{r}\neq\mathrm{0}. \\ $$$${Find}\:{a}_{{n}} \:{in}\:{terms}\:{of}\:{n}. \\…
Question Number 69502 by 20190927 last updated on 24/Sep/19 $$\int\frac{\mathrm{3sinx}+\mathrm{4cosx}}{\mathrm{4sinx}+\mathrm{3cosx}}\mathrm{dx} \\ $$ Commented by mathmax by abdo last updated on 24/Sep/19 $${let}\:{I}\:=\int\:\:\frac{\mathrm{3}{sinx}\:+\mathrm{4}{cosx}}{\mathrm{4}{sinx}\:+\mathrm{3}{cosx}}{dx}\:\:{changement}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}\:{give} \\ $$$${I}\:=\int\frac{\mathrm{3}\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }+\mathrm{4}\frac{\mathrm{1}−{t}^{\mathrm{2}}…
Question Number 69500 by TawaTawa last updated on 24/Sep/19 Answered by MJS last updated on 24/Sep/19 $$\mathrm{the}\:\mathrm{shape}\:\mathrm{of}\:\mathrm{the}\:\mathrm{graph}\:\mathrm{looks}\:\mathrm{like}\:\mathrm{a}\:\mathrm{modified} \\ $$$${f}\left({x}\right)={x}^{\mathrm{4}} −{x}^{\mathrm{2}} \\ $$$${f}\left(\mathrm{0}\right)\approx−\mathrm{7}\:\Rightarrow\:{f}\left({x}\right)\approx{x}^{\mathrm{4}} −{x}^{\mathrm{2}} −\mathrm{7} \\…
Question Number 3965 by Yozzii last updated on 25/Dec/15 $${Find}\:{det}\left({A}\right)\:{where}\:{A}\:{is}\:{an}\:{n}×{n}\:{matrix} \\ $$$${of}\:{the}\:{form}\: \\ $$$${A}=\begin{pmatrix}{\lambda}&{\mathrm{1}}&{\mathrm{1}}&{\ldots}&{\ldots}&{\ldots}&{\ldots}&{\mathrm{1}}\\{\mathrm{1}}&{\lambda}&{\mathrm{1}}&{\ldots}&{\ldots}&{\ldots}&{\ldots}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}}&{\lambda}&{\ldots}&{\ldots}&{\ldots}&{\ldots}&{\mathrm{1}}\\{\vdots}&{\vdots}&{\vdots}&{\ddots}&{\ldots}&{\ldots}&{\ldots}&{\mathrm{1}}\\{\vdots}&{\vdots}&{\vdots}&{\vdots}&{\ddots}&{\ldots}&{\ldots}&{\mathrm{1}}\\{\vdots}&{\vdots}&{\vdots}&{\vdots}&{\vdots}&{\ddots}&{\ldots}&{\mathrm{1}}\\{\vdots}&{\vdots}&{\vdots}&{\vdots}&{\vdots}&{\vdots}&{\ddots}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\lambda}\end{pmatrix} \\ $$$$\lambda={constant}\:{for}\:{leading}\:{diagonal}\:{elements} \\ $$$$\mathrm{1}{s}\:{for}\:{all}\:{other}\:{elements}. \\ $$$$ \\ $$ Commented by 123456…
Question Number 135033 by mnjuly1970 last updated on 09/Mar/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 3963 by 123456 last updated on 25/Dec/15 $${f}:\left[\mathrm{0},+\infty\right) \\ $$$${f}\left(\alpha{x}+\beta\right)=\alpha{f}\left({x}\right)+\beta \\ $$$${f}\left({x}\right)=? \\ $$ Answered by prakash jain last updated on 25/Dec/15 $${f}\left({x}\right)={x}…
Question Number 69496 by ajfour last updated on 24/Sep/19 Commented by ajfour last updated on 24/Sep/19 $${Find}\:{radius},\:{is}\:{it}\:{real}? \\ $$ Commented by mr W last updated…