Question Number 53966 by maxmathsup by imad last updated on 27/Jan/19 $${let}\:{f}\left({x}\right)\:={xsinx}\:,\mathrm{2}\pi\:{periodic}\:{even} \\ $$$${developp}\:{f}\:{at}\:{Fourier}\:{serie}\:. \\ $$ Commented by maxmathsup by imad last updated on 30/Jan/19…
Question Number 53963 by maxmathsup by imad last updated on 27/Jan/19 $${let}\:{f}\left({x}\right)\:=\:{x}\mid{x}\mid\:\:\:,\:\mathrm{2}\pi\:{periodic}\:\:{odd}\: \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie}\:. \\ $$ Commented by maxmathsup by imad last updated on 31/Jan/19…
Question Number 53958 by maxmathsup by imad last updated on 27/Jan/19 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({x}\right){ln}\left(\mathrm{1}−{x}^{\mathrm{2}} \right){dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 53956 by maxmathsup by imad last updated on 27/Jan/19 $${give}\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{−{x}} {ln}\left(\mathrm{1}−{x}\right){dx}\:\:{at}\:{form}\:{of}\:{serie} \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 53950 by maxmathsup by imad last updated on 27/Jan/19 $$\:{calculate}\:\int_{\frac{\mathrm{1}}{\mathrm{3}}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \:\:\Gamma\left({x}\right)\Gamma\left(\mathrm{1}−{x}\right){dx}\:\:\:{with}\:\Gamma\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:{t}^{{x}−\mathrm{1}} \:{e}^{−{t}} {dt}\:\:\:\:{with}\:{x}>\mathrm{0}\:. \\ $$ Commented by maxmathsup by imad…
Question Number 53931 by zambolly19 last updated on 27/Jan/19 $$\int{x}!{dx} \\ $$ Commented by maxmathsup by imad last updated on 31/Jan/19 $${sir}\:{define}\:{first}\:{x}!….. \\ $$ Terms…
Question Number 119462 by mnjuly1970 last updated on 24/Oct/20 $$\:\:\:\:\:\:\:\:\:\:…\:{advanced}\:{calculus}… \\ $$$$\:\:\:\:\:{evaluate}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\infty} \:\frac{{tan}^{−\mathrm{1}} \left({x}\right)}{{e}^{\mathrm{2}\pi{x}} −\mathrm{1}}{dx}\:=? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{m}.{n}.\mathrm{1970} \\ $$ Answered by mathmax…
Question Number 184988 by saboorhalimi last updated on 15/Jan/23 Answered by a.lgnaoui last updated on 15/Jan/23 $$\Omega=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \left({k}\mathrm{cos}\:\left({nx}\right)+{m}\mathrm{sin}\:{nx}\right){dx}+ \\ $$$$\int_{\frac{\pi}{\mathrm{2}}} ^{\pi} \left({k}\mathrm{cos}\:\left({nx}\right)+{m}\mathrm{sin}\:{nx}\right){dx} \\ $$$$=\left[\frac{{k}}{{n}}\mathrm{sin}\:{nx}−\frac{{m}}{{n}}\mathrm{cos}\:{nx}\right]_{\mathrm{0}}…
Question Number 119446 by Bird last updated on 24/Oct/20 $${calculste}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{ln}\left(\mathrm{2}+{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}^{\mathrm{3}} }{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 119442 by mnjuly1970 last updated on 24/Oct/20 $$\:\:\:\:\:\:\:\:…\:{advanced}\:\:{calculus}… \\ $$$$\:\:\:\:\:\:{prove}\:\:{that}\::\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{2}} \begin{pmatrix}{\mathrm{2}{n}}\\{{n}}\end{pmatrix}}\:\overset{???} {=}\frac{\zeta\left(\mathrm{2}\right)}{\mathrm{3}} \\ $$$${solution}::\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{2}} \ast\frac{\left(\mathrm{2}{n}\right)!}{\left({n}!\right)^{\mathrm{2}} }}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}!\ast{n}!}{{n}^{\mathrm{2}} \ast\left(\mathrm{2}{n}\right)!}\:…