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…
Question Number 61232 by maxmathsup by imad last updated on 30/May/19 $${let}\:{U}_{{n}} =\int_{\mathrm{1}} ^{+\infty} \:\:\:\frac{\left[{nx}\right]−\left[\left({n}−\mathrm{1}\right){x}\right]}{{x}^{\mathrm{3}} }\:{dx}\:\:{with}\:{n}\geqslant\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{U}_{{n}} \:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{U}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{study}\:{the}\:{serie}\:\sum_{{n}=\mathrm{1}} ^{\infty}…
Question Number 61229 by maxmathsup by imad last updated on 30/May/19 $${let}\:{f}_{{n}} \left({a}\right)\:=\int_{\mathrm{0}} ^{{a}} \:{x}^{{n}} \sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} }{dx}\:\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{let}\:{g}_{{n}} \left({a}\right)\:={f}^{'} \left({a}\right)\:\:\:{give}\:{g}_{{n}} \left({a}\right)\:{at}\:{form}\:{of}\:{integral}\:{and}\:{give}\:{its}…
Question Number 126753 by bemath last updated on 24/Dec/20 $$\:\:\int\:\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{\mathrm{3sin}\:{x}+\mathrm{4cos}\:{x}+\mathrm{1}}\:{dx}\: \\ $$ Answered by Ar Brandon last updated on 24/Dec/20 $$\mathrm{sinx}+\mathrm{cosx}=\lambda\left(\mathrm{3sinx}+\mathrm{4cosx}+\mathrm{1}\right)+\mu\left\{\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{3sinx}+\mathrm{4cosx}+\mathrm{1}\right)\right\}+\gamma \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\lambda\left(\mathrm{3sinx}+\mathrm{4cosx}+\mathrm{1}\right)+\mu\left(\mathrm{3cosx}−\mathrm{4sinx}\right)+\gamma \\ $$$$\begin{cases}{\mathrm{3}\lambda−\mathrm{4}\mu=\mathrm{1}}\\{\mathrm{4}\lambda+\mathrm{3}\mu=\mathrm{1}}\\{\lambda+\gamma=\mathrm{0}}\end{cases}\Rightarrow\begin{cases}{\mathrm{25}\mu=−\mathrm{1}}\\{\mathrm{25}\lambda=\mathrm{7}}\\{\gamma=−\lambda}\end{cases}…