Category: Integration

Question Number 50007 by Joel578 last updated on 13/Dec/18 $$\mathrm{For}a<x<b,\mathrm{find}$$$$\underset{a}{\stackrel{b}{\int }}\sqrt{x-a}.\sqrt{b-x}dx$$ Commented by Abdo msup. last updated on 13/Dec/18 $${changement}\:\sqrt{{x}−{a}}={t}\:{give}\:{x}−{a}={t}^{\mathrm{2}}…

Question Number 115533 by mnjuly1970 last updated on 26/Sep/20 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 115507 by mnjuly1970 last updated on 26/Sep/20 $$\dots .\dots matematicalanalysis\dots$$$$$$$$provethat:::$$$$a>0::\left[\begin{array}{c}i:{\int }_0^{\mathrm{\infty }}\frac{{sin}^2\left(ax\right)}{x^{\frac{3}{2}}}dx=\sqrt{\pi a}\\ ii:{\int }_0^{\mathrm{\infty }}\frac{{sin}^3\left(ax\right)}{\sqrt{x}}dx=\frac{-1+3\sqrt{3}}{4}\sqrt{\frac{\pi }{6a}}\end{array}\right]$$$$\:\:\:\:\:…

Question Number 49968 by maxmathsup by imad last updated on 12/Dec/18 $$findf\left(x\right)={\int }_0^{+\mathrm{\infty }}\frac{tarctan\left(xt\right)}{1+t^4}dt$$ Commented by mathmax by abdo last updated on…

Question Number 49954 by maxmathsup by imad last updated on 12/Dec/18 $$findf\left(\alpha \right)={\int }_0^1\frac{arctan\left(\alpha x\right)}{1+{\alpha }^2{x}^2}dx$$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{arctan}\left(\mathrm{2}{x}\right)}{\mathrm{1}+\mathrm{4}{x}^{\mathrm{2}} }\:\:{dx}\:\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{arctan}\left(\mathrm{3}{x}\right)}{\mathrm{1}+\mathrm{9}{x}^{\mathrm{2}} }\:{dx}\:. \…