Category: Integration

Question Number 59247 by maxmathsup by imad last updated on 06/May/19 $$letf\left(x\right)={\int }_0^{\frac{\pi }{2}}ln(1-xcost)dtwith\mid x\mid <1$$$$1)developpfatintegrserie$$$$2)findaexplicitformoff\left(x\right)$$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{values}\:{of}\:{integrals}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\mathrm{1}−{cost}\right){dt}\:\:{and}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\mathrm{1}+{cost}\right){dt} \…

Question Number 124742 by TANMAY PANACEA last updated on 05/Dec/20 $$\int \frac{3^t+11}{6^t+11}dt\mathit{c}\mathit{o}\mathit{l}\mathit{l}\mathit{e}\mathit{c}\mathit{t}\mathit{e}\mathit{d}\mathit{p}\mathit{r}\mathit{o}\mathit{b}\mathit{l}\mathit{e}\mathit{m}$$ Commented by MJS_new last updated on 05/Dec/20 $$\mathrm{I}\mathrm{get}\mathrm{to}\mathrm{this}\mathrm{point}:$$$$\frac{\mathrm{3}^{{t}}…

Question Number 59190 by maxmathsup by imad last updated on 05/May/19 $$find{\int }_0^1\frac{x^2}{1-cosx}dx.$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 59185 by maxmathsup by imad last updated on 09/May/19 $$calculate{\int }_0^1\frac{x}{sinx}dx$$$$letf\left(x\right)=sinx\Rightarrow f\left(x\right)=f\left(0\right)+{xf}^{{}^{\prime }}\left(0\right)+\frac{x^2}{2}{f}^{\left(2\right)}\left(0\right)+\frac{x^3}{3!}{f}^{\left(3\right)}\left(0\right)+o\left(x^4\right)$$$${but}\:{f}\left(\mathrm{0}\right)\:=\mathrm{0}\:\:\:{f}^{'} \left({x}\right)\:={cosx}\:\Rightarrow{f}^{'}…

Question Number 59175 by maxmathsup by imad last updated on 05/May/19 $$findthevalueof{\int }_0^{\mathrm{\infty }}\frac{1-cos\left(x\right)}{x^2}dx$$ Commented by maxmathsup by imad last updated on…