Category: Integration

Question Number 26564 by abdo imad last updated on 26/Dec/17 $$letgive\mathrm{\Gamma }\left(x\right)={\int }_0^{\mathrm{\infty }}{t}^{x-1}{e}^{-t}dtandx>0\left(gammaeulerfunction\right)$$$$provethat\mathrm{\Gamma }\left(x\right)={lim}_{n->\propto }\frac{(n!)n^x}{n(n+1)(n+2)\dots (n+x)}$$ Terms of Service Privacy…

Question Number 26558 by abdo imad last updated on 26/Dec/17 $$findthevalueof{\int }_0^{\mathrm{\infty }}\frac{sinx}{x(1+x^2)}dx$$ Commented by abdo imad last updated on 27/Dec/17 $${let}\:{put}\:\:{I}=\:\int_{\mathrm{0}}…

Question Number 92088 by mathmax by abdo last updated on 04/May/20 $$calculate{\int }_0^{\frac{\pi }{4}}ln\left(cosx\right)and{\int }_0^{\frac{\pi }{4}}ln\left(sinx\right)dx$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 92082 by mathmax by abdo last updated on 04/May/20 $$letf\left(\alpha \right)={\int }_0^{1}x\sqrt{x^2-x+\alpha }dxwith\alpha >\frac{1}{4}$$$$1)explicitf\left(\alpha \right)$$$$2)calculateg\left(\alpha \right)={\int }_0^1\frac{xdx}{\sqrt{x^2-x+\alpha }}$$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:{intehrals}\:\int_{\mathrm{0}} ^{\mathrm{1}}…

Question Number 92078 by mathmax by abdo last updated on 04/May/20 $$calculate{\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{cos\left(arctan(2x+1)\right)}{x^2+x+1}dx$$ Commented by abdomathmax last updated on 09/May/20 $${I}\:=\int_{−\infty}…