Category: Integration

Question Number 51186 by Abdo msup. last updated on 24/Dec/18 $$calculate{\int }_0^1\frac{\left[nx\right]}{2x+1}dx$$ Commented by Abdo msup. last updated on 25/Dec/18 $${let}\:{A}_{{n}} =\int_{\mathrm{0}}…

Question Number 116710 by ravisoni505 last updated on 06/Oct/20 Answered by maths mind last updated on 06/Oct/20 $$caseonea=0$$$$\int_{\mathrm{0}} ^{\mathrm{2}{a}} {x}^{{n}} \sqrt{\mathrm{2}{ax}−{x}^{\mathrm{2}} }{dx}=\mathrm{0} \…

Question Number 182238 by HeferH last updated on 06/Dec/22 Answered by Acem last updated on 06/Dec/22 $$a=5{\int }_0^{\mathrm{\infty }}\frac{\sin x}{x}dx=\frac{5\pi }{2}$$$$$$$$XD$$…

Question Number 116687 by megrex last updated on 05/Oct/20 $$Helpplease,tosolvethis\dots$$$$Iff\left(x\right)=1+x^{2}forx\in [-2,2]and$$$$f\left(x\right)=5otherwise.$$$$Thenwhatisthevalueof$$$${\int }_{-2}^{+2}f\left(2x^2\right)dx?$$$$ \…

Question Number 116667 by mnjuly1970 last updated on 05/Oct/20 $$\dots nicecalculus\dots$$$$$$$$veryniceintegral::$$$$demonstrate:::$$$$$$$$\:\:\:\:\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{1}−{x}}{\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} +{x}^{\mathrm{3}} \right){log}\left({x}\right)}\:{dx}\overset{???} {=}{log}\left(\sqrt{\frac{\mathrm{1}}{\mathrm{2}}}\right)…