Category: Integration

Question Number 22843 by gourav~ last updated on 22/Oct/17 $$calculatethevalueof{\int }_0^{1000}{e}^{x-\left[x\right]}dx=?$$$$where\dots .\left[x\right]isgreatestintegerfuncton$$ Answered by ajfour last updated on 23/Oct/17 $${let}\:{I}=\int_{\mathrm{0}}…

Question Number 88357 by jagoll last updated on 10/Apr/20 $$\int \underset{1}{\stackrel{4}{}}\frac{\mathrm{dx}}{(4\mathrm{x}-1)\sqrt{\mathrm{x}}}$$ Commented by john santu last updated on 10/Apr/20 $$[t=\sqrt{x},2tdt=dx]$$$$\underset{\mathrm{1}}…

Question Number 153873 by mnjuly1970 last updated on 11/Sep/21 $$$$$${\int }_0^{\mathrm{\infty }}\frac{x}{(1+x^2)(e^{2\pi x}-1)}dx=\frac{2\gamma -1}{4}$$$$$$ Commented by qaz last updated…

Question Number 88286 by Chi Mes Try last updated on 09/Apr/20 Commented by abdomathmax last updated on 09/Apr/20 $$U_n={\{{(1+\frac{1}{n})}^{n+1}-1-\frac{1}{n}\}}^{-n}$$$$\Rightarrow{U}_{{n}} ={e}^{−{nln}\left\{\:\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)^{{n}+\mathrm{1}} −\mathrm{1}−\frac{\mathrm{1}}{{n}}\right\}\:\:}…

Question Number 22689 by A1B1C1D1 last updated on 21/Oct/17 Answered by ajfour last updated on 25/Oct/17 $$={\int }_0^1\left[{\int }_0^{2x}{e}^{x^2}dy\right]dx$$$$=\int_{\mathrm{0}}…