Category: Integration

Question Number 215134 by RoseAli last updated on 29/Dec/24 Answered by Ghisom last updated on 29/Dec/24 $$\int \sqrt{x-\sqrt{x^2-4}}dx=$$$$[t=\sqrt{x-\sqrt{x^2-4}}\to dx=-\frac{2\sqrt{x^2-4}}{t}dt]$$$$=\int\left({t}^{\mathrm{2}} −\frac{\mathrm{4}}{{t}^{\mathrm{2}}…

Question Number 215091 by mnjuly1970 last updated on 28/Dec/24 $$$$$$\underset{n=0}{\sum ^{\mathrm{\infty }}}{(-1)}^n\frac{{\mathrm{\Gamma }}^2(n+1)}{\mathrm{\Gamma }(2n+1)}=?$$$$---$$$$\beta (p,q)=\frac{\mathrm{\Gamma }\left(p\right)\mathrm{\Gamma }\left(q\right)}{\mathrm{\Gamma }(p+q)}$$ Answered by MrGaster…

Question Number 215020 by mnjuly1970 last updated on 26/Dec/24 $$$$$$f:[0,1]\to \mathbb{R}isgiven.$$$$f{}^{″}iscontinuous.$$$$bythewayf\left(0\right)=f\left(1\right).$$$$provethat:$$$$$$$$\begin{array}{|c|}{\int_{\mathrm{0}} ^{\:\mathrm{1}} \left(\:{f}\:''\:\left({x}\right)\right)^{\:\mathrm{2}} {dx}\:\geqslant\:\mathrm{3}\left({f}\:'\left(\mathrm{1}\right)\right)^{\mathrm{2}}…

Question Number 214925 by efronzo1 last updated on 24/Dec/24 Commented by GDVilla last updated on 24/Dec/24 $$\mathrm{Why}\mathrm{this}\mathrm{question}\mathrm{in}\mathrm{arabic}\mathrm{translate}\mathrm{pls}$$ Answered by TonyCWX08 last updated on…

Question Number 214915 by Spillover last updated on 23/Dec/24 Answered by maths2 last updated on 23/Dec/24 $$x\to 1-x;LetAbeetheintegral$$$$={\int }_0^1\frac{dx}{(1+e^{-2+4x})(5+2x-2x^2)}\Rightarrow$$$$\mathrm{2}{A}=\int_{\mathrm{0}}…