Category: Integration

Question Number 47985 by maxmathsup by imad last updated on 17/Nov/18 $$calculateI={\int }_0^1\sqrt{1+2\sqrt{x-x^2}}dxandJ={\int }_0^1\sqrt{1-2\sqrt{x-x^2}}dx$$ Commented by MJS last updated…

Question Number 47967 by Rio Michael last updated on 17/Nov/18 $$Aparticlemovesinalinearscaresuchthatacceleration$$$$aftertsecondsisa{ms}^{-2}wherea=2t^2+t.Ifitsinitial$$$$velocitywas3{ms}^{-1}findanexpressionforS,thedistanceinmeters$$$$traveledfromstarttseconds.$$ Answered by ajfour…

Question Number 47915 by behi83417@gmail.com last updated on 16/Nov/18 Answered by MJS last updated on 16/Nov/18 $$f\left(x\right)\mathrm{is}\mathrm{kind}\mathrm{of}\mathrm{a}\mathrm{parabola}.\mathrm{I}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{think}\mathrm{we}$$$$\mathrm{can}\mathrm{find}{f}^{-1}\left(x\right)\mathrm{but}\mathrm{of}\mathrm{course}\mathrm{we}\mathrm{can}\mathrm{approximately}$$$$\mathrm{calculate}\mathrm{the}\mathrm{area}.\mathrm{area}\mathrm{between}f\mathrm{and}{f}^{-1}=$$$$=\mathrm{2}×\mathrm{area}\:\mathrm{between}\:{f}\:\mathrm{and}\:{y}={x}…

Question Number 113418 by bobhans last updated on 13/Sep/20 $$\int \frac{3\mathrm{x}-2}{\sqrt{{\mathrm{x}}^2+2\mathrm{x}+26}}\mathrm{dx}$$ Commented by bobhans last updated on 13/Sep/20 $$\mathrm{great}\mathrm{all}\mathrm{answer}..$$ Answered by…

Question Number 47851 by maxmathsup by imad last updated on 15/Nov/18 $$letf\left(x\right)=x+1+\sqrt{x}andg\left(x\right)=x+1-\sqrt{x}$$$$find\int \frac{f\left(x\right)}{g\left(x\right)}dxand\frac{\int f\left(x\right)dx}{\int g\left(x\right)dx}.$$ Commented by maxmathsup by imad last updated on 16/Nov/18…