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 $${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{sin}\left(\mathrm{2}{x}\right)}{\mathrm{1}+{ax}^{\mathrm{2}} }\:{dx}\:\:{with}\:\:\mid{a}\mid<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{approximate}\:{f}\left({a}\right)\:{by}\:{a}\:{polynom} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:\:\left({perhaps}\:{not}\:{exact}\right)\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{sin}\left(\mathrm{2}{x}\right)}{\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} }\:{dx} \\ $$$$\left.\mathrm{3}\right)\:{let}\:{g}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 61326 by maxmathsup by imad last updated on 01/Jun/19 $${find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{sinx}}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$ Commented by perlman last updated on 01/Jun/19 $${exacte}\:{value}\:!…
Question Number 192388 by sudipmoi last updated on 16/May/23 Answered by aleks041103 last updated on 22/May/23 $${p}>\mathrm{0} \\ $$$$\int_{\mathrm{1}} ^{\:\infty} \frac{{sin}\left({x}\right){dx}}{{x}^{{p}} }=\left[−\frac{{cos}\left({x}\right)}{{x}^{{p}} }\right]_{\mathrm{1}} ^{\infty} −\int_{\mathrm{1}}…
Question Number 126803 by john_santu last updated on 24/Dec/20 $$\:\:{B}\left(\frac{\mathrm{7}}{\mathrm{3}},\frac{\mathrm{2}}{\mathrm{3}}\right)\:=? \\ $$$${B}\:=\:{betha}\:{function}\: \\ $$ Answered by Dwaipayan Shikari last updated on 24/Dec/20 $${B}\left(\frac{\mathrm{7}}{\mathrm{3}},\frac{\mathrm{2}}{\mathrm{3}}\right)=\frac{\Gamma\left(\frac{\mathrm{7}}{\mathrm{3}}\right)\Gamma\left(\frac{\mathrm{2}}{\mathrm{3}}\right)}{\Gamma\left(\mathrm{3}\right)}=\frac{\Gamma\left(\frac{\mathrm{1}}{\mathrm{3}}\right)\Gamma\left(\frac{\mathrm{2}}{\mathrm{3}}\right).\frac{\mathrm{4}}{\mathrm{3}}.\frac{\mathrm{1}}{\mathrm{3}}}{\mathrm{2}!}=\frac{\mathrm{2}}{\mathrm{9}}.\frac{\pi}{{sin}\frac{\pi}{\mathrm{3}}}=\frac{\mathrm{4}\pi}{\mathrm{9}\sqrt{\mathrm{3}}} \\ $$…
Question Number 126788 by john_santu last updated on 24/Dec/20 $$\:\sigma\:=\:\underset{\mathrm{0}} {\overset{\:\:\:\:\:\infty} {\int}}\sqrt{{x}}\:{e}^{−{x}/\mathrm{4}} \:{dx}\:=\:?\: \\ $$ Answered by Ar Brandon last updated on 24/Dec/20 $$\mathrm{x}=\mathrm{u}^{\mathrm{2}} \:\Rightarrow\:\mathrm{dx}=\mathrm{2udu}…
Question Number 61240 by Tawa1 last updated on 30/May/19 $$\int\:\frac{\mathrm{x}^{\mathrm{2}\:} −\:\mathrm{4}}{\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{4}\right)^{\mathrm{2}} }\:\mathrm{dx} \\ $$ Commented by maxmathsup by imad last updated on 31/May/19 $${let}\:{A}\:=\int\:\:\frac{{x}^{\mathrm{2}}…
Question Number 61237 by aliesam last updated on 30/May/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 126766 by mnjuly1970 last updated on 24/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…{calculus}\:\:\left({I}\right)… \\ $$$$\:\:\:\:{please}\:\:{evaluate}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Psi=\int_{\mathrm{0}} ^{\:\mathrm{1}} \left(\:\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{6}} }\:\right){dx}=? \\ $$$$ \\ $$ Answered by Ar Brandon…