Category: Integration

Question Number 171727 by cortano1 last updated on 20/Jun/22 Answered by mahdipoor last updated on 20/Jun/22 $$y⩾\frac{x^2+y^2}{2}\Rightarrow 1⩾x^2+{(y-1)}^2\Rightarrow -1⩽x⩽1$$$${for}\:{x}={x}_{\mathrm{0}} \:,\:{max}\left({x}_{\mathrm{0}} +{y}\right)={x}_{\mathrm{0}}…

Question Number 40625 by Raj Singh last updated on 25/Jul/18 Answered by MJS last updated on 25/Jul/18 $$\int \frac{dx}{\sqrt{x}+\sqrt[3]{x}}=$$$$[t=\sqrt[6]{x}\to dx=6\sqrt[6]{x^5}dt]$$$$=\mathrm{6}\int\frac{{t}^{\mathrm{3}} }{{t}+\mathrm{1}}{dt}=\mathrm{6}\int\left({t}^{\mathrm{2}} −{t}+\mathrm{1}−\frac{\mathrm{1}}{{t}+\mathrm{1}}\right){dt}=…

Question Number 40621 by math khazana by abdo last updated on 25/Jul/18 $$letf\left(x\right)={\int }_0^{\frac{\pi }{2}}ln(1+xcos\theta )d\theta$$$$1)calculatef\left(1\right)$$$$2)findasimpleformoff\left(x\right)$$$$3)developpfatontehrserie$$ Answered by…

Question Number 40620 by math khazana by abdo last updated on 25/Jul/18 $$find\int ((x+1)\sqrt{1+x^2}+(1+x^2)\sqrt{x+1})dx$$ Answered by tanmay.chaudhury50@gmail.com last updated on 25/Jul/18 $$\int{x}\sqrt{\mathrm{1}+{x}^{\mathrm{2}}…

Question Number 106132 by mathmax by abdo last updated on 02/Aug/20 $$\mathrm{find}{\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}{\mathrm{x}}^2{\mathrm{e}}^{-{\mathrm{x}}^2}\ln (1+{\mathrm{x}}^2)\mathrm{dx}$$$$$$ Terms of Service…