Category: Integration

Question Number 70602 by oyemi kemewari last updated on 06/Oct/19 $$\mathrm{I}={\int }_0^{\mathrm{\infty }}\ln (\sqrt{1-\mathrm{x}}+\sqrt{1+\mathrm{x}})\mathrm{dx}$$ Commented by mathmax by abdo last updated on 06/Oct/19 $${error}\:{in}\:{the}\:{question}\:{the}\:{function}\:{x}\rightarrow\sqrt{\mathrm{1}−{x}}+\sqrt{\mathrm{1}+{x}}\:{is}\:{defined}\:{on}…

Question Number 136132 by frc2crc last updated on 19/Mar/21 $$Findaseriesfor\frac{x^2}{\tanh \left(x\pi \right)\tan \left(x\pi \right)}$$ Answered by Dwaipayan Shikari last updated on 19/Mar/21 $${sinh}\left(\pi{x}\right)=\pi{x}\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\mathrm{1}+\frac{{x}^{\mathrm{2}} }{{n}^{\mathrm{2}}…

Question Number 5058 by Yozzii last updated on 06/Apr/16 $$\int \int \frac{a}{(1-lnx)(lny-1)}dxdy=?$$ Commented by Yozzii last updated on 06/Apr/16 $$\int\int\int\int…\int\int\int\frac{{a}}{\underset{{i}=\mathrm{1}} {\overset{{n}} {\prod}}\left(\mathrm{1}−{lnx}_{{i}} \right)}{dx}_{\mathrm{1}} {dx}_{\mathrm{2}} …{dx}_{{n}}…

Question Number 5032 by gourav~ last updated on 04/Apr/16 $$\int \frac{ax+b}{{(cx+d)}^2}dx=?$$$$$$ Answered by Yozzii last updated on 04/Apr/16 $${Let}\:{u}={cx}+{d}\Rightarrow{du}={cdx}\Rightarrow{c}^{−\mathrm{1}} {du}={dx}. \…

Question Number 136076 by physicstutes last updated on 18/Mar/21 $$\mathrm{find}\mathrm{the}\mathrm{area}\mathrm{between}\mathrm{the}\mathrm{curve}y=3+2x-x^2,\mathrm{the}x-\mathrm{axis}$$$$\mathrm{and}\mathrm{the}\mathrm{line}y=3.$$$$\mathrm{find}\mathrm{the}\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{solid}\mathrm{generated}\mathrm{when}\mathrm{the}\mathrm{curve}\mathrm{is}$$$$\mathrm{rotated}\mathrm{completely}\mathrm{about}\mathrm{the}\mathrm{line}y=3$$ Answered by mr W last updated…