Category: Integration

Question Number 127885 by psyche last updated on 02/Jan/21 $$\int \left(\frac{\sin ({2\tan }^{-1}\left(x\right)+x)}{x}\right)thelimit[0,\mathrm{\infty })$$ Answered by Lordose last updated on 02/Jan/21 $$$$$$\Omega\:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{sin}\left(\mathrm{2tan}^{−\mathrm{1}}…

Question Number 62342 by maxmathsup by imad last updated on 20/Jun/19 $$letf\left(\xi \right)=\int \frac{x^2}{\sqrt{1-\xi x^2}}dxwith0<\xi <1$$$$1)determineaexplicitformoff\left(\xi \right)$$$$2)calculate{lim}_{\xi \to 1}f\left(\xi \right)$$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \:\frac{{x}^{\mathrm{2}} }{\:\sqrt{\mathrm{1}−{sin}^{\mathrm{2}} \theta\:{x}^{\mathrm{2}}…

Question Number 62335 by maxmathsup by imad last updated on 19/Jun/19 $$1)calculatef(x,y)={\int }_0^{\mathrm{\infty }}\frac{e^{-xt}cos\left(yt\right)}{\sqrt{t}}dtandg(x,y)={\int }_0^{\mathrm{\infty }}\frac{e^{-xt}sin\left(yt\right)}{\sqrt{t}}dt$$$$withx>0andy>0$$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\frac{{e}^{−\mathrm{2}{t}} \:{cos}\left({t}\right)}{\:\sqrt{{t}}}\:{dt}\:{and}\:\int_{\mathrm{0}}…

Question Number 127857 by slahadjb last updated on 02/Jan/21 $$\int \sqrt{x}{e}^{x}dx?$$ Commented by Dwaipayan Shikari last updated on 02/Jan/21 $$\int{x}^{\frac{\mathrm{1}}{\mathrm{2}}} \underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{x}^{{n}}…

Question Number 127833 by Algoritm last updated on 02/Jan/21 Answered by mathmax by abdo last updated on 02/Jan/21 $$\mathrm{I}={\int }_0^4\frac{\mathrm{cosx}}{\sqrt{4-\mathrm{x}}}\mathrm{dx}\mathrm{we}\mathrm{do}\mathrm{the}\mathrm{changement}\sqrt{4-\mathrm{x}}=\mathrm{t}\Rightarrow 4-\mathrm{x}={\mathrm{t}}^2$$$$\mathrm{I}\:=\int_{\mathrm{2}} ^{\mathrm{0}} \:\frac{\mathrm{cos}\left(\mathrm{4}−\mathrm{t}^{\mathrm{2}}…