Category: Integration

Question Number 42708 by prof Abdo imad last updated on 01/Sep/18 $$calculatef\left(\alpha \right)={\int }_0^{\mathrm{\infty }}\frac{e^{-2x}-e^{-x}}{x^2}{e}^{-\alpha x^2}dxwith\alpha >0$$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{e}^{−\mathrm{2}{x}} \:−{e}^{−{x}} }{{x}^{\mathrm{2}}…

Question Number 42704 by maxmathsup by imad last updated on 01/Sep/18 $$f\left(x\right)=\frac{e^{3x}+e^{-3x}}{2}$$$$1)determine{f}^{-1}\left(x\right)$$$$2)calculate{\int }_0^{1}xf\left(x\right)dxand{\int }_0^{1}f\left(x\right)dx$$$$\left.\mathrm{3}\right)\:\:{calculate}\:\:\:\int\:\:{f}^{−\mathrm{1}}…

Question Number 42680 by prof Abdo imad last updated on 31/Aug/18 $$calculale{A}_n\left(\alpha \right)={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{cos\left(\alpha x^n\right)}{1+x^2}dxwith$$$$nintegrnatural.$$$$$$ Commented by…

Question Number 108175 by bemath last updated on 15/Aug/20 Commented by bemath last updated on 15/Aug/20 $$aman6feettallwalksatarate6feet$$$$persecondawayfromalightthat$$$$is15feetabovetheground.$$$$Whenheis10feetfromthebaseofthelight$$$${at}\:{what}\:{rate}\:{is}\:{the}\:{tip}\:{of}\:{his}\:{shadow}…

Question Number 108169 by bemath last updated on 15/Aug/20 $$\frac{✓\mathcal{B}e\mathcal{M}ath✓}{\succ \prec }$$$$\int \frac{x^5-x}{x^8-1}dx?$$ Answered by Dwaipayan Shikari last updated on 15/Aug/20 $$\int\frac{{x}\left({x}^{\mathrm{4}}…