Question Number 125858 by bramlexs22 last updated on 14/Dec/20 Commented by mr W last updated on 14/Dec/20 $$\mathrm{13}×\mathrm{26}×\mathrm{2}×\mathrm{62}.\mathrm{4}×\mathrm{1}=\mathrm{42}\:\mathrm{182}\:{ft}−{lb} \\ $$ Commented by bramlexs22 last updated…
Question Number 60320 by Sardor2211 last updated on 19/May/19 Commented by maxmathsup by imad last updated on 20/May/19 $${let}\:{I}\:=\int\:\:\frac{{x}^{\mathrm{3}} −\mathrm{5}{x}^{\mathrm{2}} \:+\mathrm{5}{x}\:+\mathrm{23}}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)\left({x}−\mathrm{5}\right)}{dx}\:\:{let}\:{decompose}\:{F}\left({x}\right)\:=\frac{{x}^{\mathrm{3}} −\mathrm{5}{x}^{\mathrm{2}} \:+\mathrm{5}{x}\:+\mathrm{23}}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)\left({x}−\mathrm{5}\right)}…
Question Number 60318 by Sardor2211 last updated on 19/May/19 Commented by kaivan.ahmadi last updated on 20/May/19 $${we}\:{find}\:{I}=\int{x}^{\mathrm{2}} {arctgx}\:{dx}\:{then}\:{multiply}\:\mathrm{4} \\ $$$${u}={arctgx}\Rightarrow{du}=\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$$${dv}={x}^{\mathrm{2}} {dx}\Rightarrow{v}=\frac{{x}^{\mathrm{3}} }{\mathrm{3}}…
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Question Number 60311 by aliesam last updated on 19/May/19 $$\int\frac{{dx}}{\:\sqrt{{sec}\:{h}^{\mathrm{2}} \left({x}\right)+\mathrm{1}}}\:{dx} \\ $$ Commented by MJS last updated on 20/May/19 $$\mathrm{sech}\:{x}=\frac{\mathrm{1}}{\mathrm{cosh}\:{x}} \\ $$ Commented by…
Question Number 125841 by bramlexs22 last updated on 14/Dec/20 $${Given}\:{f}\left({x}\right)={f}\left({x}+\mathrm{2}\right)\:\forall{x}\in\mathbb{R} \\ $$$${if}\:\underset{\mathrm{0}} {\overset{\mathrm{2}} {\int}}{f}\left({x}\right){dx}={k}\:{then}\:\underset{\mathrm{0}} {\overset{\mathrm{1010}} {\int}}{f}\left({x}+\mathrm{2}{a}\right){dx}\:? \\ $$$${for}\:{a}\in\mathbb{Z}\: \\ $$ Commented by mr W last…
Question Number 191369 by mnjuly1970 last updated on 23/Apr/23 $$ \\ $$$$\:\:\:{calculate} \\ $$$$ \\ $$$$\:\:\:\:\:\boldsymbol{\phi}=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\:{sin}\left(\frac{{n}\pi}{\mathrm{3}}\:\right)}{\left(\mathrm{2}{n}\:+\:\mathrm{1}\:\right)^{\:\mathrm{2}} }=\:? \\ $$$$ \\ $$ Answered by…
Question Number 191342 by mnjuly1970 last updated on 23/Apr/23 $$ \\ $$$$\:\:\:\:{calculate}… \\ $$$$\:\Omega\:=\left\{\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \left(\:\:\mathrm{1}\:+\:\sqrt{\mathrm{3}}\:{sin}\left({x}\right)\:+\:{cos}\left({x}\right)\:\right)^{\:{n}} {dx}\right\}^{\frac{\mathrm{1}}{{n}}} =\:? \\ $$$$ \\ $$$$ \\ $$ Answered…
Question Number 60264 by maxmathsup by imad last updated on 19/May/19 $${let}\:{f}\left({t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{e}^{−\mathrm{3}\:\left[{x}^{\mathrm{2}} \right]} }{{x}^{\mathrm{2}} \:+{t}^{\mathrm{2}} }{dx}\:\:{with}\:{t}>\mathrm{0} \\ $$$$\mathrm{1}.\:{determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({t}\right) \\ $$$$\mathrm{2}.\:{find}\:{also}\:{g}\left({t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−\mathrm{3}\left[{x}^{\mathrm{2}} \right]}…
Question Number 60263 by maxmathsup by imad last updated on 19/May/19 $${let}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{e}^{−{n}\left[{x}^{\mathrm{2}} \right]} }{{x}^{\mathrm{2}} +\mathrm{3}}\:{dx}\: \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{n}\:{U}_{{n}} \\…