Question Number 34225 by abdo imad last updated on 03/May/18 $${find}\:\int\:\:\:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{2}} +{x}^{\mathrm{4}} } \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 03/May/18 $$\int\frac{\mathrm{1}}{{x}^{\mathrm{4}} +{x}^{\mathrm{2}\:} +\mathrm{1}}{dx}…
Question Number 34222 by abdo imad last updated on 03/May/18 $${let}\:{give}\:{the}\:{sequence}\:{of}\:{integrals} \\ $$$${J}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:{x}^{{n}} \:\:{e}^{−\frac{{x}^{\mathrm{2}} }{\mathrm{2}}} {dx} \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:{J}_{{n}} =\left({n}−\mathrm{1}\right){J}_{{n}−\mathrm{2}} \:\:\:\forall{n}\geqslant\mathrm{2} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{J}_{\mathrm{2}{p}}…
Question Number 34223 by abdo imad last updated on 03/May/18 $${find}\:\int\:\:\:\frac{{dx}}{{x}^{\mathrm{2}{n}} −\mathrm{1}}\:\:{with}\:{n}\:{integr}\:{natural}\:{and}\:{n}\geqslant\mathrm{1}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34220 by abdo imad last updated on 03/May/18 $${calculate}\:{I}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{cosx}\:{ln}\left({tanx}\right){dx}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34221 by abdo imad last updated on 03/May/18 $${study}\:{the}\:{convergence}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{\sqrt{\mathrm{1}−{x}}}{{x}}\:{dx}\:. \\ $$ Commented by math khazana by abdo last updated on 04/May/18…
Question Number 34218 by abdo imad last updated on 02/May/18 $${find}\:\int\sqrt{{tanx}}{dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{6}}} \sqrt{{tanx}}\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34219 by abdo imad last updated on 03/May/18 $${calculate}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\:\:\frac{{dx}}{{cos}^{\mathrm{3}} {x}\:+{sin}^{\mathrm{3}} {x}} \\ $$ Commented by abdo imad last updated on 31/May/18…
Question Number 34216 by abdo imad last updated on 02/May/18 $${let}\:{give}\:{I}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left({x}+\mathrm{1}\right)}{{x}}{dx}\:{and}\:{J}\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}−{x}\right)}{{x}}{dx} \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{the}\:{existence}\:{of}\:{I}\:{and}\:{J} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{I}\:+{J}\:{and}\:\mathrm{2}{I}\:+{J} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{I}\:{and}\:{J}\:. \\ $$ Terms of…
Question Number 165273 by mnjuly1970 last updated on 28/Jan/22 $$ \\ $$$$\:\:\:\:\:\:{lim}_{\:{n}\rightarrow\:\infty} \:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\:{n}\:.\:{e}^{\:\mathrm{1}−\:{x}^{\:\mathrm{2}} } }{\:\mathrm{1}\:+\:{n}^{\:\mathrm{2}} \:{x}^{\:\mathrm{2}} }\:{dx}\:=? \\ $$$$\:\:\:\:\:\:\:\:\:\:−−−−−− \\ $$ Answered by…
Question Number 165271 by mnjuly1970 last updated on 28/Jan/22 $$ \\ $$$$\:\:\:\:\:\mathrm{L}{et}\:,\:\:\:{f}\::\:\left[\:\mathrm{0}\:,\:\mathrm{1}\:\right]\:\rightarrow\:\mathbb{R}\:\:{is}\:{a}\:{continuous}\: \\ $$$$\:\:\:\:{function}\:,\:{prove}\:{that}\::\:\:\: \\ $$$$\:\:\:\:\:\:\:\:{lim}_{\:{n}\rightarrow\:\infty} \:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{n}\:{f}\left({x}\right)}{\mathrm{1}+\:{n}^{\mathrm{2}} \:{x}^{\:\mathrm{2}} }\:{dx}\:=\:\frac{\pi}{\mathrm{2}}\:{f}\:\left(\mathrm{0}\:\right) \\ $$$$\:\:\:\:\:−−−\:{proof}\:−−− \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{S}_{\:{n}}…