Category: Integration

Question Number 59282 by Mr X pcx last updated on 07/May/19 $$calculatef\left(x\right)={\int }_0^{\mathrm{\infty }}{e}^{-x\left[t\right]}sin\left(\left[t\right]\right)dt$$$$withx>0$$$$2)calculate{\int }_0^{\mathrm{\infty }}{e}^{-3\left[t\right]}sin\left(\left[t\right]\right)dt.$$ Commented…

Question Number 59277 by Mr X pcx last updated on 07/May/19 $$calculate{\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{ln(1+x^2)}{1+x^2}dx$$ Commented by maxmathsup by imad last updated…

Question Number 59274 by Mr X pcx last updated on 07/May/19 $$calculate{\int }_0^{1}arctan(1+x+x^2)dx$$ Commented by maxmathsup by imad last updated on…

Question Number 124794 by benjo_mathlover last updated on 06/Dec/20 $$Iff\left(x\right)=\{\begin{array}{l}2x;0<x<1\\ 3;x=1\\ 6x-1;1<x<2\end{array}$$$$find\underset{0}{\stackrel{2}{\int }}f\left(x\right)dx?$$ Answered by TITA last updated on 06/Dec/20 $$\int_{\mathrm{0}} ^{\mathrm{2}}…

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} \…