Category: Integration

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} \…

Question Number 168894 by mnjuly1970 last updated on 20/Apr/22 Commented by mahdipoor last updated on 20/Apr/22 $$\int \frac{1}{12}(\frac{3-x}{x^2+x}+\frac{x-2}{x^2+2x+4})dx=$$$$\int\frac{{dx}}{\left({x}^{\mathrm{2}} +{x}\right)\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{4}\right)}=\int\frac{{d}\left({lnx}\right)}{\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{4}\right)}= \…