Category: Integration

Question Number 206890 by mathzup last updated on 29/Apr/24 $$cansomeonefindtheexactvalueof$$$$\sum _{n=0}^{\mathrm{\infty }}\frac{1}{{(n!)}^2}$$ Commented by Frix last updated on 30/Apr/24 $$\mathrm{This}\:\mathrm{is}\:\mathrm{a}\:\mathrm{Modified}\:\mathrm{Bressel}\:\mathrm{Function}\:\mathrm{of}\:\mathrm{the}…

Question Number 206829 by 2kdw last updated on 27/Apr/24 $$\oint \frac{x}{x+2}{dx}^{2}iswrong?$$ Commented by mr W last updated on 27/Apr/24 $$therearethingstowhichyoucan$$$${say}\:{they}\:{are}\:{wrong},\:{for}\:{example} \…

Question Number 206789 by BaliramKumar last updated on 25/Apr/24 Answered by A5T last updated on 25/Apr/24 $$\sqrt[n]{a_1{a}_2\dots a_n}=P$$$$\sqrt[{\mathrm{2}{n}}]{{a}_{{n}+\mathrm{1}} {a}_{{n}+\mathrm{2}} …{a}_{\mathrm{3}{n}} }={Q}…

Question Number 206754 by mathzup last updated on 23/Apr/24 $$find{\int }_0^1\sqrt{1-\sqrt{x}}{ln}^2\left(x\right)dx$$ Answered by Berbere last updated on 24/Apr/24 $${x}={u}^{\mathrm{2}} \Rightarrow{dx}=\mathrm{2}{udu} \…

Question Number 206645 by Red1ight last updated on 21/Apr/24 $$\mathrm{Let}f\left(x\right)=x(x-10)$$$$\mathrm{and}\mathrm{let}\mathrm{A}\mathrm{be}\mathrm{the}\mathrm{region}\mathrm{enclosed}\mathrm{within}$$$$\mathrm{the}\mathrm{following}\mathrm{points}$$$$(2,7),(8,7),(2,4),(8,4)$$$$\mathrm{what}\mathrm{is}\mathrm{the}\mathrm{average}\mathrm{arc}\mathrm{length}\mathrm{of}\mathrm{a}\cdot f\left(x\right)$$$$\mathrm{inside}\mathrm{A},a\in {\mathbb{R}}^{-}$$ Commented by mr…