Question Number 128570 by mnjuly1970 last updated on 08/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{mathematical}\:\:{analysis}… \\ $$$$\:\:{if}\:''\:\:{f}\:\:\:''\:\:{is}\:\mathscr{R}{eimann}\:{integrable} \\ $$$$\:\:\:{function}\:\:{on}\:\left[{a}\:,\:{b}\:\right]\:,\:{then}\:{prove}:: \\ $$$$\:\:\:\:\: \\ $$$$\:\:{lim}_{{t}\rightarrow\infty\:} \left\{\int_{{a}} ^{\:{b}} {f}\left({x}\right){cos}\left({tx}\right){dx}\:\right\}=\mathrm{0} \\ $$$$\:\:..\mathscr{R}{eimann}−\mathscr{L}{ebesgue}\:\:{theorem}… \\ $$$$…
Question Number 128575 by Study last updated on 08/Jan/21 $$\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} \\ $$$$\frac{\left({x}+\mathrm{2}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{13}}}{\mathrm{2}}+\frac{\mathrm{9}}{\mathrm{2}}\mathrm{ln}\:\left({x}+\mathrm{2}+\sqrt{{x}^{\mathrm{2}}…
Question Number 63034 by mathmax by abdo last updated on 28/Jun/19 $${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \left({ln}\left({cosx}\right)\right)^{\mathrm{2}} \:{dx}\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 63032 by mathmax by abdo last updated on 28/Jun/19 $${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 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 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 $$\mathrm{0}\:{is}\:{a}\:{double}\:{pole}\:\Rightarrow{Res}\left({f},\mathrm{0}\right)\:={lim}_{{z}\rightarrow\mathrm{0}}…
Question Number 63026 by mathmax by abdo last updated on 27/Jun/19 $${calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{sin}\left(\mathrm{2}{x}\right)}{\mathrm{2}{cosx}\:−\mathrm{3}{sinx}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 63023 by mathmax by abdo last updated on 27/Jun/19 $${calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{x}^{\mathrm{2}} −\mathrm{3}}{{x}^{\mathrm{4}} \:+{x}^{\mathrm{2}} \:+\mathrm{1}}{dx}\:. \\ $$ Commented by mathmax by abdo last…
Question Number 128542 by bramlexs22 last updated on 08/Jan/21 $$\:\int\:\frac{\left(\mathrm{x}^{\mathrm{4}} −\mathrm{x}\right)^{\mathrm{1}/\mathrm{4}} }{\mathrm{x}^{\mathrm{5}} }\:\mathrm{dx}\:=? \\ $$ Answered by liberty last updated on 08/Jan/21 $$\:\gamma=\int\:\frac{\mathrm{x}\left(\mathrm{1}−\mathrm{x}^{−\mathrm{3}} \right)^{\mathrm{1}/\mathrm{4}} }{\mathrm{x}^{\mathrm{5}}…
Question Number 128540 by bramlexs22 last updated on 08/Jan/21 $$\mathrm{If}\:\mathrm{f}\left(\mathrm{x}\right)=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{x}^{\mathrm{n}} −\mathrm{x}^{−\mathrm{n}} }{\mathrm{x}^{\mathrm{n}} +\mathrm{x}^{−\mathrm{n}} }\:,\mathrm{x}>\mathrm{1} \\ $$$$\mathrm{then}\:\int\:\frac{\mathrm{xf}\left(\mathrm{x}\right)\:\mathrm{ln}\:\left(\mathrm{x}+\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:\right)}{\:\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }}\:\mathrm{dx}\:=? \\ $$ Commented by liberty last…