Category: Integration

Question Number 104910 by Dwaipayan Shikari last updated on 24/Jul/20 $${\int }_0^1\frac{1}{\sqrt{1+x^3}}dx$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 39374 by maxmathsup by imad last updated on 05/Jul/18 $$calculateI={\int }_0^{\mathrm{\infty }}\frac{arctan\left(x^2\right)}{1+x^2}dx$$ Commented by math khazana by abdo last…

Question Number 39370 by maxmathsup by imad last updated on 05/Jul/18 $$letI\left(\lambda \right)={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{cos\left(\lambda x\right)}{{(1+ix)}^2}dx$$$$1)extractRe\left(I\left(\lambda \right)\right)andIm\left(I\left(\lambda \right)\right)$$$$2)calculateI\left(\lambda \right)$$$$3)concludethevaluesofRe\left(I\left(\lambda \right)\right)andIm\left(I\left(\lambda \right)\right).$$ Commented by…

Question Number 39368 by maxmathsup by imad last updated on 05/Jul/18 $$letF\left(t\right)={\int }_0^{+\mathrm{\infty }}\frac{sinx}{x(1+x^2)}{e}^{-tx(1+x^2)}dxwitht⩾0$$$$1)caculate\frac{dF}{dt}\left(t\right)$$$$2)findasimpleformofF\left(t\right)$$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{sinx}}{{x}\left(\mathrm{1}+{x}^{\mathrm{2}}…

Question Number 104890 by Ar Brandon last updated on 24/Jul/20 $$\underset{\mathrm{n}\to \mathrm{\infty }}{\lim }\frac{1}{\mathrm{n}}\underset{\mathrm{k}=1}{\sum ^{\mathrm{n}}}{[1+\frac{{\mathrm{k}}^3}{{\mathrm{n}}^3}]}^{-\frac{1}{2}}$$ Answered by abdomathmax last updated on 24/Jul/20…