Question Number 39381 by rahul 19 last updated on 05/Jul/18 Answered by ajfour last updated on 06/Jul/18 $${f}\:'\left({x}\right)\geqslant\left[{f}\left({x}\right)\right]^{\mathrm{3}} +\left[{f}\left({x}\right)\right]^{−\mathrm{1}} \\ $$$${and}\:{f}\left(\mathrm{0}\right)=\mathrm{1}\:,\:\:{f}\left({a}\right)=\mathrm{3}^{\mathrm{1}/\mathrm{4}} \\ $$$$\Rightarrow\:\:\:\int_{\mathrm{1}} ^{\:\:{y}} \frac{{dy}}{{y}^{\mathrm{3}}…
Question Number 39382 by rahul 19 last updated on 05/Jul/18 Answered by ajfour last updated on 06/Jul/18 $$\int_{\alpha} ^{\:\:\beta} {f}\left({x}\right){g}'\left({x}\right){dx}\:=\left[{f}\left({x}\right){g}\left({x}\right)\right]_{\alpha} ^{\beta} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:−\int_{\alpha} ^{\:\:\beta} {f}\:'\left({x}\right){g}\left({x}\right){dx}…
Question Number 39379 by rahul 19 last updated on 05/Jul/18 Commented by MJS last updated on 06/Jul/18 $$\left(\mathrm{1}\right)\:\:\:\:\:\mid\mid{x}\mid−\mid{y}\mid\mid=\mathrm{1} \\ $$$$\left(\mathrm{2}\right)\:\:\:\:\:\mathrm{2}{a}\mid{x}\mid\mid{y}\mid+\mathrm{1}=\mathrm{2}\mid{x}\mid+{a}\mid{y}\mid \\ $$$$\left(\mathrm{1}\right)\:\:\:\:\:\begin{cases}{\left.{y}_{\mathrm{1}} \left.=−\mid{x}\mid−\mathrm{1};\:\mathrm{range}\left({y}_{\mathrm{1}} \right)=\right]−\infty;\:−\mathrm{1}\right]}\\{{y}_{\mathrm{2}} =\mid{x}\mid+\mathrm{1};\:\mathrm{range}\left({y}_{\mathrm{2}}…
Question Number 104910 by Dwaipayan Shikari last updated on 24/Jul/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{3}} }}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 39373 by maxmathsup by imad last updated on 05/Jul/18 $${find}\:{the}\:{values}\:{of}\:{integrals} \\ $$$${A}\:=\:\int_{−\infty} ^{+\infty} \:{cos}\left({x}^{\mathrm{2}} \:+{x}+\mathrm{1}\right){dx}\:\:\:{and}\:{B}\:=\:\int_{−\infty} ^{+\infty} \:{sin}\left({x}^{\mathrm{2}} \:+{x}+\mathrm{1}\right){dx} \\ $$ Commented by math…
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…
1-calculate-F-x-1-x-arctan-t-t-2-dt-with-x-1-2-calculate-A-n-1-n-arctan-t-t-2-dt-and-find-lim-n-A-n-
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}}…