Category: Integration

Question Number 126139 by mnjuly1970 last updated on 17/Dec/20 $$$$$$closedformula\dots .$$$${\int }_0^1\frac{x^{n}ln\left(x\right)}{1+x}dx=?$$$$$$ Commented by Dwaipayan Shikari…

Question Number 60595 by maxmathsup by imad last updated on 22/May/19 $$letf\left(a\right)={\int }_0^1\frac{{ln}^2\left(x\right)}{{(1-ax)}^2}dxwith\mid a\mid <1$$$$1)findaexplicitformoff\left(a\right)$$$$\left.\mathrm{2}\right)\:{determine}\:{A}\left(\theta\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}^{\mathrm{2}} \left({x}\right)}{\left(\mathrm{1}−\left({cos}\theta\right){x}\right)^{\mathrm{2}} }{dx}\:\:{with}\:\mathrm{0}<\theta<\frac{\pi}{\mathrm{2}} \…

Question Number 126073 by benjo_mathlover last updated on 17/Dec/20 Commented by benjo_mathlover last updated on 17/Dec/20 $$Thegraphofthedifferentiable$$$$functiongwithdomain-6⩽x⩽2is$$$$showninthefigureabove.Theareas$$$$oftheregionsboundedbythex-axis$$$${and}\:{the}\:{graph}\:{of}\:{g}\:{on}\:{the}\:{intervals}\:\left[−\mathrm{6},−\mathrm{5}\right]…

Question Number 126068 by benjo_mathlover last updated on 17/Dec/20 Answered by liberty last updated on 17/Dec/20 $$h\left(x\right)={\int }_1^{x}f\left(t\right)dt\iff h\left(1\right)={\int }_1^{1}f\left(t\right)dt=0$$ Terms of…

Question Number 60506 by prof Abdo imad last updated on 21/May/19 $$calculate\int {\int }_W\frac{\sqrt{2x^2+3y^2}}{x+y}dxdy$$$$withW=\{(x,y)\in R^2/0<x<1and0<y<1.$$ Commented by Mr X pcx…