Question Number 39374 by maxmathsup by imad last updated on 05/Jul/18 $${calculate}\:{I}\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{arctan}\left({x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$ Commented by math khazana by abdo last…
Question Number 39375 by rahul 19 last updated on 05/Jul/18 Commented by rahul 19 last updated on 06/Jul/18 $$?????? \\ $$ Terms of Service Privacy…
Question Number 39370 by maxmathsup by imad last updated on 05/Jul/18 $${let}\:{I}\:\left(\lambda\right)\:=\:\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{cos}\left(\lambda{x}\right)}{\left(\mathrm{1}+{ix}\right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{1}\right)\:\:{extract}\:{Re}\left({I}\left(\lambda\right)\right)\:{and}\:{Im}\left({I}\left(\lambda\right)\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{I}\left(\lambda\right) \\ $$$$\left.\mathrm{3}\right)\:{conclude}\:\:{the}\:{values}\:{of}\:{Re}\left({I}\left(\lambda\right)\right)\:{and}\:{Im}\left({I}\left(\lambda\right)\right). \\ $$ Commented by…
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Question Number 39369 by maxmathsup by imad last updated on 05/Jul/18 $$\left.\mathrm{1}\right)\:{calculate}\:{F}\left({x}\right)=\:\int_{\mathrm{1}} ^{\sqrt{{x}}} \:\:\:\frac{{arctan}\left({t}\right)}{{t}^{\mathrm{2}} }{dt}\:\:\:{with}\:{x}\geqslant\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\:{A}_{{n}} =\:\int_{\mathrm{1}} ^{\sqrt{{n}}} \:\:\frac{{arctan}\left({t}\right)}{{t}^{\mathrm{2}} }\:{dt}\:\:{and}\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$ Commented…
Question Number 39368 by maxmathsup by imad last updated on 05/Jul/18 $${let}\:{F}\left({t}\right)=\:\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{{sinx}}{{x}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}\:{e}^{−{tx}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)} {dx}\:\:{witht}\geqslant\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{caculate}\:\:\frac{{dF}}{{dt}}\left({t}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{a}\:{simple}\:{form}\:{of}\:{F}\left({t}\right) \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{sinx}}{{x}\left(\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 39357 by Cheyboy last updated on 05/Jul/18 $$\int\:\frac{\mathrm{1}}{{xln}\left({x}+\mathrm{1}\right)}\:{dx} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 104890 by Ar Brandon last updated on 24/Jul/20 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{\mathrm{n}}\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\left[\mathrm{1}+\frac{\mathrm{k}^{\mathrm{3}} }{\mathrm{n}^{\mathrm{3}} }\right]^{−\frac{\mathrm{1}}{\mathrm{2}}} \\ $$ Answered by abdomathmax last updated on 24/Jul/20…
Question Number 39342 by rahul 19 last updated on 05/Jul/18 $$\mathrm{Let}\:\mathrm{f}\left({x}\right)\:=\:\int_{\mathrm{0}\:} ^{\mathrm{2}} \:\mid{x}−{t}\mid\:\mathrm{dt}\:\left({x}>\mathrm{0}\right)\:,\:\mathrm{then} \\ $$$$\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{f}\left({x}\right)\:\mathrm{is}\:? \\ $$ Answered by MrW3 last updated on 05/Jul/18 $${for}\:\mathrm{0}<{x}\leqslant\mathrm{2}:…
Question Number 39341 by rahul 19 last updated on 05/Jul/18 $$\mathrm{I}_{\mathrm{1}} =\:\int_{\mathrm{0}} ^{\pi} \frac{\mathrm{sin}\:\mathrm{884}{x}\:\mathrm{sin}\:\mathrm{1122}{x}}{\mathrm{sin}\:{x}}\:{dx} \\ $$$$\mathrm{I}_{\mathrm{2}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{x}^{\mathrm{238}} \left({x}^{\mathrm{1768}} −\mathrm{1}\right)}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)}\:{dx} \\ $$$${then}\:{value}\:{of}\:\frac{\mathrm{I}_{\mathrm{1}} }{\mathrm{I}_{\mathrm{2}}…
Question Number 39338 by rahul 19 last updated on 05/Jul/18 $$\mathrm{If}\:\mathrm{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{4}} \:\mathrm{e}^{\mid\mathrm{t}−{x}\mid} \:\mathrm{dt}\:\:\:\:\left(\mathrm{0}\leqslant{x}\leqslant\mathrm{4}\right), \\ $$$$\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{f}\left({x}\right)\:\mathrm{is}\:=\:? \\ $$ Commented by math khazana by abdo last…