Category: Integration

Question Number 37896 by abdo mathsup 649 cc last updated on 19/Jun/18 $$let{I}_n={\int }_0^n\frac{{(-1)}^{\left[x\right]}}{{(2x+1)}^2}dx$$$$1)calculate{I}_{n}intermsofn$$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{I}_{{n}} \…

Question Number 37895 by abdo mathsup 649 cc last updated on 19/Jun/18 $$calculate{A}_n={\int }_0^n(x-\left[\sqrt{x}\right])dxand$$$${lim}_{n\to +\mathrm{\infty }}{A}_n$$ Answered by tanmay.chaudhury50@gmail.com last…

Question Number 37889 by abdo mathsup 649 cc last updated on 19/Jun/18 $$calculate{\int }_0^{\mathrm{\infty }}\frac{arctan\left(2x\right)}{x}{e}^{-tx}dxwitht⩾0$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 37887 by abdo mathsup 649 cc last updated on 19/Jun/18 $$findf\left(\alpha \right)={\int }_0^{1}arctan(1+e^{-\alpha x})dxwith\alpha ⩾0$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 37884 by prof Abdo imad last updated on 18/Jun/18 $$letI={\int }_0^{\mathrm{\infty }}{e}^{-\left[x\right]}{cos}^2\left(2\pi x\right)dxand$$$$J={\int }_0^{\mathrm{\infty }}{e}^{-\left[x\right]}{sin}^2\left(2\pi x\right)dx$$$$\left.\mathrm{1}\right)\:{calculate}\:{I}\:+{J}\:{and}\:{I}\:−{J} \…