Question Number 55672 by gunawan last updated on 01/Mar/19 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{complex}\:\mathrm{integral} \\ $$$$\int_{\mid{z}\mid=\mathrm{1}} \left({z}^{\mathrm{2}} \mathrm{sin}\:\frac{\mathrm{1}}{{z}}+\frac{\mathrm{1}}{{z}^{\mathrm{2}} }\mathrm{sin}\:{z}\right)\:{dz}\:\mathrm{is}… \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 55668 by mr W last updated on 01/Mar/19 $${Find}\:{all}\:{functions}\:{y}={f}\left({x}\right)\:{such}\:{that} \\ $$$${y}'{y}''={y}'''. \\ $$ Commented by malwaan last updated on 02/Mar/19 $$\mathrm{y}=\mathrm{e}^{\mathrm{x}} \\ $$…
Question Number 186736 by Rupesh123 last updated on 09/Feb/23 Answered by Frix last updated on 09/Feb/23 $$\lfloor\frac{\mathrm{2}^{\mathrm{0}} }{\mathrm{3}}\rfloor=\mathrm{0}\:\Rightarrow \\ $$$${A}_{\mathrm{2}{n}} =\underset{{i}=\mathrm{1}} {\overset{\mathrm{2}{n}} {\sum}}\lfloor\frac{\mathrm{2}^{{i}} }{\mathrm{3}}\rfloor=\underset{{i}=\mathrm{1}} {\overset{{n}}…
Question Number 121203 by benjo_mathlover last updated on 05/Nov/20 $$\:\int\:\frac{\mathrm{cos}\:^{\mathrm{5}} \left(\mathrm{x}\right)}{\:\sqrt{\mathrm{sin}\:\left(\mathrm{x}\right)}}\:\mathrm{dx}\: \\ $$ Answered by MJS_new last updated on 06/Nov/20 $$\int\frac{\mathrm{cos}^{\mathrm{5}} \:{x}}{\:\sqrt{\mathrm{sin}\:{x}}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{\mathrm{sin}\:{x}}\:\rightarrow\:{dx}=\frac{\mathrm{2}\sqrt{\mathrm{sin}\:{x}}}{\mathrm{cos}\:{x}}{dt}\right] \\…
Question Number 186735 by Rupesh123 last updated on 09/Feb/23 Answered by Ar Brandon last updated on 09/Feb/23 $${I}=\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{ln}\left(\frac{\mathrm{1}}{{x}}\right)\right)^{\mathrm{2023}} {dx}\:,\:{t}=−\mathrm{ln}{x}\:\Rightarrow{x}={e}^{−{t}} \\ $$$$\:\:=\int_{\mathrm{0}} ^{\infty} {t}^{\mathrm{2023}}…
Question Number 186726 by Rupesh123 last updated on 09/Feb/23 Answered by cortano12 last updated on 09/Feb/23 $${f}\:'\left({x}\right)=\frac{\mathrm{3}{x}^{\mathrm{2}} }{\mathrm{1}+\mathrm{ln}\:{x}^{\mathrm{3}} }=\frac{\mathrm{3}{x}^{\mathrm{2}} }{\mathrm{ln}\:{ex}^{\mathrm{3}} } \\ $$$${f}\:''\left({x}\right)=\:\frac{\mathrm{6}{x}.\mathrm{ln}\:{ex}^{\mathrm{3}} −\frac{\mathrm{3}{ex}^{\mathrm{2}} }{{ex}^{\mathrm{3}}…
Question Number 121174 by benjo_mathlover last updated on 05/Nov/20 $$\underset{−\pi/\mathrm{2}} {\overset{\pi/\mathrm{2}} {\int}}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{ln}\:\left(\frac{\pi+\mathrm{x}}{\pi−\mathrm{x}}\right)\right)\mathrm{cos}\:\mathrm{x}\:\mathrm{dx}\:? \\ $$ Answered by TANMAY PANACEA last updated on 05/Nov/20 $${I}=\int_{\frac{−\pi}{\mathrm{2}}} ^{\frac{\pi}{\mathrm{2}}}…
Question Number 55638 by gunawan last updated on 01/Mar/19 $$\mathrm{For}\:\mathrm{all}\:{n}\:\in\:\mathbb{N} \\ $$$${f}_{{n}} \left({x}\right)=\begin{cases}{\frac{{nx}}{\mathrm{2}{n}−\mathrm{1}},\:\:\:\:\:{x}\:\in\:\left[\mathrm{0},\:\frac{\mathrm{2}{n}−\mathrm{1}}{{n}}\right]}\\{\mathrm{1}\:\:\:\:\:\:\:\:\:\:,\:\:\:\:\:\:{x}\:\in\left[\frac{\mathrm{2}{n}−\mathrm{1}}{{n}},\:\mathrm{2}\right]}\end{cases} \\ $$$$\mathrm{then}\:\mathrm{for}\:{n}\rightarrow\infty \\ $$$$\int_{\mathrm{1}} ^{\mathrm{2}} {f}_{{n}} \left({x}\right)\:{dx}\:\mathrm{convergences}\:\mathrm{to}.. \\ $$$$ \\ $$ Answered…
Question Number 121164 by mnjuly1970 last updated on 05/Nov/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\mathrm{ADVANCED}\:\:\mathrm{CALCULUS}… \\ $$$$\:\:\:\:\mathrm{If}\:\:\:\int_{\mathrm{0}} ^{\:\infty} {ln}\left({x}\right){sin}\left({x}^{\mathrm{2}} \right){dx}\:=\lambda\int_{\mathrm{0}} ^{\:\infty} {sin}\left({x}^{\mathrm{2}} \right){dx}\: \\ $$$$\:\:\:\:\:\:\:\:{then}\:\:{find}\:\:{the}\:\:{value}\:{of}\:''\lambda''\:. \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\mathrm{m}.\mathrm{n}.\mathrm{july}.\mathrm{1970}… \\…
Question Number 55615 by Abdo msup. last updated on 28/Feb/19 $${let}\:{F}\left(\alpha\right)=\int_{\alpha} ^{\mathrm{1}+\alpha^{\mathrm{2}} } \:\:\frac{{sin}\left(\alpha{x}\right)}{\mathrm{1}+\alpha{x}^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\frac{{dF}}{{d}\alpha}\left(\alpha\right) \\ $$$$\left.\mathrm{2}\right)\:\:{calculate}\:{lim}_{\alpha\rightarrow\mathrm{0}} \:\:{F}\left(\alpha\right) \\ $$ Answered by tanmay.chaudhury50@gmail.com…