Question Number 61388 by maxmathsup by imad last updated on 02/Jun/19 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{sin}\left({lnx}\right)}{{lnx}}\:{dx}\:. \\ $$ Commented by perlman last updated on 02/Jun/19 $${let}\:{u}={ln}\left({x}\right) \\…
Question Number 61386 by maxmathsup by imad last updated on 02/Jun/19 $${find}\:{the}\:{value}\:{of}\:\int_{−\infty} ^{+\infty} \:\:\frac{{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx} \\ $$ Commented by perlman last updated on 02/Jun/19…
Question Number 192453 by Spillover last updated on 18/May/23 $${Find}\:\:\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\mathrm{1}}{{n}^{\mathrm{2}} }+\frac{\mathrm{2}}{{n}^{\mathrm{2}} }+\frac{\mathrm{3}}{{n}^{\mathrm{2}} }+…\frac{{n}}{{n}^{\mathrm{2}} }\right) \\ $$ Answered by senestro last updated on 18/May/23 $$\mathrm{1}/\mathrm{2}…
Question Number 192452 by Spillover last updated on 18/May/23 $${Evaluate}\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{2}^{{x}\:} {dx}\:\:\: \\ $$$$ \\ $$ Answered by senestro last updated on 18/May/23 $$\mathrm{1}/\mathrm{ln}\:\mathrm{2}…
Question Number 192454 by Spillover last updated on 18/May/23 $${Evaluate}\:{the}\:{following}\:{improper}\:{intergrals} \\ $$$$\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{sec}\:{xdx}\:\:{if}\:{it}\:{convergent} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 61349 by tanmay last updated on 01/Jun/19 Commented by MJS last updated on 01/Jun/19 $$…\mathrm{harder}\:\mathrm{than}\:\mathrm{I}\:\mathrm{thought} \\ $$$$\int\frac{\sqrt{{t}^{\mathrm{2}} −\mathrm{5}}}{{t}−{a}}{dt}= \\ $$$$\:\:\:\:\left[{t}=\frac{\sqrt{\mathrm{5}}}{\mathrm{sin}\:{u}}\:\Leftrightarrow\:{u}=\mathrm{arcsin}\:\frac{\sqrt{\mathrm{5}}}{{t}}\:\rightarrow\:{dt}=−\frac{{t}\sqrt{{t}^{\mathrm{2}} −\mathrm{5}}}{\:\sqrt{\mathrm{5}}}{du}\right] \\ $$$$\:\:\:\:\:\mathrm{now}\:\mathrm{the}\:\mathrm{root}\:\mathrm{is}\:\mathrm{gone},\:\mathrm{but}\:\mathrm{we}\:\mathrm{must}\:\mathrm{make}…
Question Number 126879 by bramlexs22 last updated on 25/Dec/20 $$\:\int\:\frac{{x}^{\mathrm{4}} }{\mathrm{1}+{x}^{\mathrm{8}} }\:{dx}\:? \\ $$ Answered by Lordose last updated on 25/Dec/20 $$\Omega\:=\:\int^{\:} \frac{\mathrm{x}^{\mathrm{4}} }{\mathrm{1}+\mathrm{x}^{\mathrm{8}} }\mathrm{dx}\:=\:\underset{\mathrm{n}=\mathrm{0}}…
Question Number 126873 by mathmax by abdo last updated on 25/Dec/20 $$\mathrm{calculate}\:\int_{\mathrm{2019}} ^{\mathrm{2021}} \:\:\:\frac{\mathrm{dx}}{\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2019}} \left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2021}} } \\ $$ Answered by Ar Brandon last updated on…
Question Number 126865 by Lordose last updated on 24/Dec/20 $$\int_{\mathrm{0}} ^{\:\pi} \frac{\mathrm{x}}{\mathrm{2}+\mathrm{cos}\left(\mathrm{2x}\right)}\mathrm{dx}\:=\:\mathrm{0} \\ $$$$\mathrm{Prove}\:\mathrm{or}\:\mathrm{Disprove} \\ $$ Commented by Ar Brandon last updated on 25/Dec/20 Commented…
Question Number 61328 by maxmathsup by imad last updated on 01/Jun/19 $${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{sin}\left(\mathrm{2}{x}\right)}{\mathrm{1}+{ax}^{\mathrm{2}} }\:{dx}\:\:{with}\:\:\mid{a}\mid<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{approximate}\:{f}\left({a}\right)\:{by}\:{a}\:{polynom} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:\:\left({perhaps}\:{not}\:{exact}\right)\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{sin}\left(\mathrm{2}{x}\right)}{\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} }\:{dx} \\ $$$$\left.\mathrm{3}\right)\:{let}\:{g}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}}…