Category: Integration

Question Number 33896 by math khazana by abdo last updated on 26/Apr/18 $$let\mathrm{\Gamma }\left(x\right)={\int }_0^{\mathrm{\infty }}{t}^{x-1}{e}^{-t}dt$$$$1)find\mathrm{\Gamma }(x+1)intermsof\mathrm{\Gamma }\left(x\right)withx>0$$$$2)calculate\mathrm{\Gamma }\left(n\right)forn\in N^{★}$$$$3)calculate\mathrm{\Gamma }\left(\frac{3}{2}\right).$$…

Question Number 33895 by math khazana by abdo last updated on 26/Apr/18 $$let\mathrm{\Gamma }\left(x\right)={\int }_0^{\mathrm{\infty }}{t}^{x-1}{e}^{-t}dtwithx>0$$$$1)provethat\mathrm{\Gamma }\left(x\right)\mathrm{\Gamma }(1-x)=\frac{\pi }{sin\left(\pi x\right)}$$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{x}^{\mathrm{2}} } {dx}\:.…

Question Number 33885 by math khazana by abdo last updated on 26/Apr/18 $$developpatintegrserief\left(x\right)={\int }_0^{x}sin\left(t^2\right)dt.$$ Commented by prof Abdo imad last updated…

Question Number 33884 by math khazana by abdo last updated on 26/Apr/18 $$letF\left(x\right)={\int }_0^{\frac{\pi }{2}}\frac{arctan\left(xtant\right)}{tant}dtfindasimple$$$$formoff\left(x\right).$$$$2)findthevalueof{\int }_0^{\frac{\pi }{2}}\frac{arctan\left(2tant\right)}{tant}dt.$$ Commented by…

Question Number 99413 by maths mind last updated on 20/Jun/20 $${\int }_0^{+\mathrm{\infty }}\frac{sin\left(ax\right)}{e^{2\pi x}-1}dx$$ Answered by mathmax by abdo last updated on 20/Jun/20…