Category: Integration

Question Number 211006 by universe last updated on 26/Aug/24 Answered by mr W last updated on 26/Aug/24 $$=0becauseofoddfunction{zy}^2$$ Commented by mr W last…

Question Number 210969 by universe last updated on 24/Aug/24 $$\mathrm{if}{\mathrm{a}}_{\mathrm{n}}={\mathrm{n}}^4{\int }_{\mathrm{n}}^{\mathrm{n}+1}\frac{\mathrm{x}\mathrm{dx}}{1+{\mathrm{x}}^5}\mathrm{then}$$$$\left(1\right)\mathrm{\Sigma }{\mathrm{a}}_{\mathrm{n}}\mathrm{is}\mathrm{convergent}\mathrm{or}\mathrm{divergent}??$$$$\left(2\right)\underset{\mathrm{n}\to \mathrm{\infty }}{\lim }{\mathrm{a}}_{\mathrm{n}}=??$$ Terms…

Question Number 210917 by depressiveshrek last updated on 22/Aug/24 $$\mathrm{Find}\mathrm{the}\mathrm{area}\mathrm{intersected}\mathrm{by}\mathrm{three}$$$$\mathrm{circles}\mathrm{of}\mathrm{radius}1,\mathrm{centered}\mathrm{at}\mathrm{the}$$$$\mathrm{origin},\mathrm{at}(1,0)\mathrm{and}(1,1)\mathrm{respectively}.$$ Answered by mr W last updated on 22/Aug/24 Commented…

Question Number 210820 by Ghisom last updated on 19/Aug/24 $$\mathrm{prove}$$$$\underset{0}{\stackrel{\mathrm{\infty }}{\int }}\frac{\arctan \sqrt{x^2+2}}{(x^2+1)\sqrt{x^2+2}}dx=\frac{{\pi }^2}{12}$$ Answered by BHOOPENDRA last updated…

Question Number 210601 by mnjuly1970 last updated on 13/Aug/24 $$$$$$$$$$Findthevalueof:$$$$$$$$\:\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }} \:\int_{\sqrt{\:{x}^{\:\mathrm{2}} \:+{y}^{\:\mathrm{2}} }}…