Category: Integration

Question Number 48078 by cesar.marval.larez@gmail.com last updated on 19/Nov/18 Answered by tanmay.chaudhury50@gmail.com last updated on 19/Nov/18 $$21)\int e^{2-x}dx$$$$t=2-xdt=-dx$$$$\int e^t\times -dt$$$$=\left(−\mathrm{1}\right){e}^{{t}}…

Question Number 113600 by eric last updated on 14/Sep/20 $$Prouverque$$$$\beta (a,b)=\frac{\mathrm{\Gamma }\left(a\right)\mathrm{\Gamma }\left(b\right)}{\mathrm{\Gamma }(a+b)}={\int }_0^1{x}^{a-1}{(1-x)}^{b-1}dx$$ Answered by Dwaipayan Shikari last updated on…

Question Number 48063 by maxmathsup by imad last updated on 18/Nov/18 $$letW\left(x\right)={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{arctan\left({xt}^2\right)}{2+t^2}dt$$$$1)findaexplicitformoff\left(x\right)$$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{−\infty} ^{+\infty} \:\:\:\:\frac{{t}^{\mathrm{2}} }{\left(\mathrm{2}+{t}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{\mathrm{2}} {t}^{\mathrm{4}}…

Question Number 48057 by F_Nongue last updated on 18/Nov/18 Commented by maxmathsup by imad last updated on 18/Nov/18 $${I}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{\mathrm{1}−{x}}{\mathrm{2}−{x}\:+\mathrm{3}−{x}}{dx}\:+\int_{\mathrm{1}} ^{\mathrm{2}} \:\:\frac{{x}−\mathrm{1}}{\mathrm{2}−{x}\:+\mathrm{3}−{x}}\:+\int_{\mathrm{2}} ^{\mathrm{3}} \:\:\frac{{x}−\mathrm{1}}{{x}−\mathrm{2}\:+\mathrm{3}−{x}}\:+\int_{\mathrm{3}}…

Question Number 48043 by maxmathsup by imad last updated on 18/Nov/18 $$letf\left(\alpha \right)={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{cos\left(\alpha x^3\right)}{x^2+8}dx$$$$1)calculatef\left(\alpha \right)$$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{−\infty} ^{+\infty} \:\:\frac{{cos}\left(\mathrm{2}{x}^{\mathrm{3}} \right)}{{x}^{\mathrm{2}} \:+\mathrm{8}}{dx}\:. \…