Question Number 127679 by 676597498 last updated on 31/Dec/20 $${its}\:\mathrm{9}:\mathrm{30}{pm}\:{in}\:{Cameroon} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 62145 by maxmathsup by imad last updated on 16/Jun/19 $${calculate}\:\:\int_{\mathrm{0}} ^{\pi} {ln}\left({x}^{\mathrm{2}} −\mathrm{2}{xsin}\theta\:+\mathrm{1}\right){d}\theta \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 62141 by maxmathsup by imad last updated on 15/Jun/19 $${let}\:{A}\:=\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:−{i}\right)^{\mathrm{2}} }\:\:\:\:\:\left(\:{i}^{\mathrm{2}} =−\mathrm{1}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A} \\ $$$$\left.\mathrm{2}\right)\:{let}\:{R}\:={Re}\left({A}\right)\:{and}\:{I}\:={Im}\left({A}\right) \\ $$$${find}\:\:{the}\:{value}\:{of}\:{R}\:{and}\:{I}\:. \\ $$…
Question Number 62128 by maxmathsup by imad last updated on 15/Jun/19 $${let}\:{U}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({nx}\right)}{\left({x}^{\mathrm{2}} \:+{n}^{\mathrm{2}} \right)^{\mathrm{3}} }{dx}\:\:{with}\:{n}\geqslant\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \:{intrems}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} {n}\:{U}_{{n}} \\…
Question Number 62122 by aliesam last updated on 15/Jun/19 $$\int{e}^{{cos}\left({x}\right)} {sin}\left({sin}\left({x}\right)\right)\:{dx}\: \\ $$ Commented by MJS last updated on 15/Jun/19 $$\int\mathrm{e}^{\mathrm{cos}\:{x}} \mathrm{sin}\:\mathrm{sin}\:{x}\:{dx}=−\frac{\mathrm{i}}{\mathrm{2}}\int\left(\mathrm{e}^{\frac{\mathrm{e}^{\mathrm{i}{x}} −\mathrm{e}^{−\mathrm{i}{x}} }{\mathrm{2}}} −\mathrm{e}^{−\frac{\mathrm{e}^{\mathrm{i}{x}}…
Question Number 127631 by snipers237 last updated on 31/Dec/20 $${Let}\:{f}\in{C}^{\infty} \left(\mathbb{R},\mathbb{R}\right)\:,\:\forall\:{n}\in\mathbb{N}\:\:\:{M}_{{n}} =\mid\mid{f}^{\left({n}\right)} \mid\mid_{\infty} \:\: \\ $$$${and}\:\:{u}_{{n}} =\frac{\mathrm{2}^{{n}−\mathrm{1}} {M}_{{n}} }{{M}_{{n}−\mathrm{1}} }\:\:\:{for}\:{n}\geqslant\mathrm{1}\: \\ $$$${Show}\:{that}\:{if}\:\:\:{M}_{\mathrm{1}} <\sqrt{\mathrm{2}{M}_{\mathrm{0}} {M}_{\mathrm{2}} }\:{then}\:{u}_{{n}}…
Question Number 127616 by bramlexs22 last updated on 31/Dec/20 $$\:\mathrm{If}\:\int_{\mathrm{1}} ^{\:\mathrm{4}} \mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:=\:\mathrm{6}\:,\:\mathrm{then}\:\int_{\mathrm{1}} ^{\:\mathrm{4}} \mathrm{f}\left(\mathrm{5}−\mathrm{x}\right)\:\mathrm{dx}\:?\: \\ $$ Commented by liberty last updated on 31/Dec/20 $$\:\mathrm{let}\:\mathrm{5}−\mathrm{x}\:=\:\mathrm{X}\:\Rightarrow\mathrm{dx}\:=\:−\mathrm{dX}\: \\…
Question Number 127618 by bramlexs22 last updated on 31/Dec/20 $$\:\int\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{2021}} \left(\mathrm{1}+\mathrm{x}^{\mathrm{2020}} \right)}\:?\: \\ $$ Answered by Dwaipayan Shikari last updated on 31/Dec/20 $$\int\frac{\mathrm{1}}{{x}^{\mathrm{2021}} }−\frac{\mathrm{1}}{{x}\left(\mathrm{1}+{x}^{\mathrm{2020}} \right)}{dx}=−\frac{{x}^{−\mathrm{2020}}…
Question Number 127604 by Algoritm last updated on 31/Dec/20 Answered by Lordose last updated on 31/Dec/20 Commented by Algoritm last updated on 31/Dec/20 $$? \\…
Question Number 127605 by pticantor last updated on 31/Dec/20 $${find}\:{arg}\left({z}\right) \\ $$$${where}\:\boldsymbol{{z}}=\mathrm{1}+\boldsymbol{{cos}}\alpha+{icos}\beta \\ $$ Answered by MJS_new last updated on 31/Dec/20 $$\mathrm{arg}\:\left(\mathrm{1}+\mathrm{cos}\:\alpha\:+\mathrm{i}\:\mathrm{cos}\:\beta\right)\:= \\ $$$$=\frac{\pi}{\mathrm{2}}\mathrm{sign}\:\left(\mathrm{cos}\:\beta\right)\:−\mathrm{arctan}\:\frac{\mathrm{1}+\mathrm{cos}\:\alpha}{\mathrm{cos}\:\beta} \\…