Question Number 99326 by 175 last updated on 20/Jun/20 Answered by abdomathmax last updated on 20/Jun/20 $$\mathrm{at}\:\mathrm{form}\:\mathrm{of}\:\mathrm{serie} \\ $$$$\mathrm{I}\:=\int\:\:\frac{\mathrm{e}^{\mathrm{2x}} \:\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} −\mathrm{5x}−\mathrm{4}} }{\mathrm{1}−\mathrm{e}^{\mathrm{x}−\mathrm{x}^{\mathrm{2}} −\mathrm{5x}−\mathrm{4}} }\:\mathrm{dx}\:=\int\:\:\frac{\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} −\mathrm{3x}−\mathrm{4}}…
Question Number 33787 by Joel578 last updated on 24/Apr/18 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\mathrm{1}}{{n}}\:\underset{\mathrm{1}} {\overset{{n}} {\int}}\:{n}^{\frac{\mathrm{1}}{{x}}} \:{dx}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 164853 by mnjuly1970 last updated on 22/Jan/22 $$ \\ $$$$\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{ln}\left(\mathrm{1}+{x}\:\right).{ln}\left({x}\right)}{\mathrm{1}−{x}}\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 164854 by Zaynal last updated on 22/Jan/22 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{Evaluate}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{Integral}}; \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left[\int_{\mathrm{0}} ^{\infty} \:\frac{\boldsymbol{{x}}^{\mathrm{2}} \:−\:\mathrm{1}}{\mathrm{1}−\boldsymbol{{x}}}\:\boldsymbol{{dx}}\:=??\right] \\ $$$$\:\:\:\:\:\:\:\:\:\:\:^{\left\{\boldsymbol{{Z}}.\mathrm{A}\right\}} \\ $$ Answered by MJS_new last updated on…
Question Number 99315 by bramlex last updated on 20/Jun/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 33759 by 33 last updated on 24/Apr/18 $${solve}\::\: \\ $$$$\:\underset{−\pi/\mathrm{2}} {\overset{\pi/\mathrm{2}} {\int}}\:\:\frac{{sin}\:\theta\:}{\:\sqrt{\:{R}^{\mathrm{2}} \:+\:{r}^{\mathrm{2}} \:−\:\mathrm{2}{rR}\:{cos}\:\theta}}\:{d}\theta \\ $$ Commented by MJS last updated on 24/Apr/18…
Question Number 33747 by sma3l2996 last updated on 23/Apr/18 $${Calculate}\:\int_{−\infty} ^{+\infty} {e}^{−{x}^{\mathrm{2}} } {dx}\:\:{using}\:\:{Residue}\:{theorem} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 99278 by Rio Michael last updated on 19/Jun/20 $$\:{x}\:\:\:\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}\:\:\:\:\:\:\:\:\:\mathrm{4}\:\:\:\:\:\:\:\:\:\:\mathrm{6}\:\:\:\:\:\:\:\:\:\mathrm{8}\:\:\:\:\:\:\:\:\:\:\mathrm{10} \\ $$$$\:{f}\left({x}\right)\:\:\mathrm{2}.\mathrm{4}\:\:\:\:\:\:\:\mathrm{3}.\mathrm{6}\:\:\:\:\:\:\mathrm{4}.\mathrm{9}\:\:\:\:\:\mathrm{6}.\mathrm{9}\:\:\:\:\:\mathrm{8}.\mathrm{0}\:\:\:\:\:\:\:\:\mathrm{11}.\mathrm{9} \\ $$$$\mathrm{Given}\:\mathrm{the}\:\mathrm{curve}\:{y}\:=\:{f}\left({x}\right),\:\mathrm{with}\:\mathrm{corresponding}\:\mathrm{values}\:\mathrm{of} \\ $$$${f}\left({x}\right)\:\mathrm{at}\:\mathrm{certain}\:{x}\:\mathrm{values}.\:\mathrm{The}\:\mathrm{curve}\:{y}\:=\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{rotated} \\ $$$$\mathrm{at}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{2}\pi\:\mathrm{about}\:\mathrm{the}\:\mathrm{x}−\mathrm{axis}.\:\mathrm{Find}\: \\ $$$$\left(\mathrm{1}\right)\:\mathrm{The}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{surface}\:\mathrm{generated}\:\mathrm{using}\:\mathrm{simpson}'\mathrm{s}\:\mathrm{rule}. \\ $$$$\left(\mathrm{2}\right)\:\mathrm{The}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{surface}\:\mathrm{generated}\:\mathrm{using}\:\mathrm{simpson}'\mathrm{s}\:\mathrm{rule}. \\ $$…
Question Number 33744 by prof Abdo imad last updated on 23/Apr/18 $${let}\:\:{P}_{{n}} \left({x}\right)=\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{\mathrm{4}} \right)….\left(\mathrm{1}+{x}^{\mathrm{2}^{{n}} } \right) \\ $$$${calculate}\:\:{lim}_{{n}\rightarrow+\infty} \int_{\mathrm{0}} ^{{x}} \:{P}_{{n}} \left({t}\right){dt}\:\:{with}\:\:\mathrm{0}<{x}<\mathrm{1}\:. \\ $$…
Question Number 164809 by mathlove last updated on 22/Jan/22 $$\left.\mathrm{1}\right)\:\:\:\:\int\frac{\sqrt[{\mathrm{3}}]{{x}}}{\:\sqrt{{x}}+\sqrt[{\mathrm{4}}]{{x}}}=? \\ $$$$\left.\mathrm{2}\right)\:\:\:\:\int\frac{{x}}{\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{2}\right)^{\mathrm{2}} }=? \\ $$ Answered by Ar Brandon last updated on 22/Jan/22 $$\mathrm{Ostrogradsky}…