Question Number 128575 by Study last updated on 08/Jan/21 $$\int\sqrt{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{13}}{dx}=?? \\ $$ Commented by MJS_new last updated on 08/Jan/21 $$\mathrm{use}\:\mathrm{formula}\:\mathrm{for}\:\int\sqrt{{x}^{\mathrm{2}} +{ax}+{b}}\:{dx}\:!!!\:\mathrm{to}\:\mathrm{get} \\ $$$$\frac{\left({x}+\mathrm{2}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{13}}}{\mathrm{2}}+\frac{\mathrm{9}}{\mathrm{2}}\mathrm{ln}\:\left({x}+\mathrm{2}+\sqrt{{x}^{\mathrm{2}}…
Question Number 128570 by mnjuly1970 last updated on 08/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{mathematical}\:\:{analysis}… \\ $$$$\:\:{if}\:''\:\:{f}\:\:\:''\:\:{is}\:\mathscr{R}{eimann}\:{integrable} \\ $$$$\:\:\:{function}\:\:{on}\:\left[{a}\:,\:{b}\:\right]\:,\:{then}\:{prove}:: \\ $$$$\:\:\:\:\: \\ $$$$\:\:{lim}_{{t}\rightarrow\infty\:} \left\{\int_{{a}} ^{\:{b}} {f}\left({x}\right){cos}\left({tx}\right){dx}\:\right\}=\mathrm{0} \\ $$$$\:\:..\mathscr{R}{eimann}−\mathscr{L}{ebesgue}\:\:{theorem}… \\ $$$$…
Question Number 63034 by mathmax by abdo last updated on 28/Jun/19 $${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \left({ln}\left({cosx}\right)\right)^{\mathrm{2}} \:{dx}\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 63033 by mathmax by abdo last updated on 28/Jun/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sin}^{\mathrm{2}} \left({x}\right)}{{x}^{\mathrm{2}} \left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{dx}\: \\ $$ Commented by mathmax by abdo last…
Question Number 63032 by mathmax by abdo last updated on 28/Jun/19 $${let}\:{f}\left({z}\right)\:=\frac{\mathrm{1}}{{sin}\left(\pi{z}\right)}\:\:{calculate}\:{Res}\left({f},{n}\right)\:{with}\:{n}\:{integr} \\ $$ Commented by mathmax by abdo last updated on 28/Jun/19 $${z}={n}\:{is}\:{simple}\:{pole}\:{for}\:{f}\:\Rightarrow{Res}\left({f},{n}\right)\:={lim}_{{z}\rightarrow{n}} \frac{{z}−{n}}{{sin}\left(\pi{z}\right)}…
Question Number 128566 by Dwaipayan Shikari last updated on 08/Jan/21 $$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{1}}{\mathrm{2}}.\frac{\mathrm{1}}{\mathrm{1}!}\right)^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{3}}\left(\frac{\mathrm{1}.\mathrm{3}}{\mathrm{2}^{\mathrm{2}} }.\frac{\mathrm{1}}{\mathrm{2}!}\right)^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{4}}\left(\frac{\mathrm{1}.\mathrm{3}.\mathrm{5}}{\mathrm{2}^{\mathrm{3}} }.\frac{\mathrm{1}}{\mathrm{3}!}\right)^{\mathrm{2}} +…=_{\mathrm{2}} {F}_{\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{2}},\frac{\mathrm{1}}{\mathrm{2}};\mathrm{2};\mathrm{1}\right)=\frac{\mathrm{4}}{\pi} \\ $$ Commented by Dwaipayan Shikari last…
Question Number 63031 by mathmax by abdo last updated on 28/Jun/19 $${let}\:{f}\left({z}\right)\:=\frac{{sin}\left({z}\right)}{{z}^{\mathrm{2}} }\:\:{calculate}\:{Res}\left({f},\mathrm{0}\right) \\ $$ Commented by mathmax by abdo last updated on 28/Jun/19 $$\mathrm{0}\:{is}\:{a}\:{double}\:{pole}\:\Rightarrow{Res}\left({f},\mathrm{0}\right)\:={lim}_{{z}\rightarrow\mathrm{0}}…
Question Number 128567 by mnjuly1970 last updated on 08/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:\:{calculus}… \\ $$$$\:{prove}\:{that}:::: \\ $$$$\:\:\:\phi=\int_{\mathrm{0}} ^{\:\infty} {sin}\left({x}^{\mathrm{2}} \right){sin}\left({x}^{−\mathrm{2}} \right){dx} \\ $$$$\:\:\:\:\:=\frac{\mathrm{1}}{\mathrm{4}}\sqrt{\frac{\pi}{\mathrm{2}}}\:\left({e}^{−\mathrm{2}} +{sin}\left(\mathrm{2}\right)−{cos}\left(\mathrm{2}\right)\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$…
Question Number 63026 by mathmax by abdo last updated on 27/Jun/19 $${calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{sin}\left(\mathrm{2}{x}\right)}{\mathrm{2}{cosx}\:−\mathrm{3}{sinx}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 128561 by 777316 last updated on 08/Jan/21 Answered by Dwaipayan Shikari last updated on 08/Jan/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}{cosx}+\left(\frac{\mathrm{1}−{cosx}}{{sinx}}\right)=\mathrm{1}+\frac{\mathrm{2}{sin}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}}{{sinx}}=\mathrm{1} \\ $$ Terms of Service…