Category: Integration

Question Number 67942 by mhmd last updated on 02/Sep/19 $$\int e^{y^2/2}dy$$ Commented by mr W last updated on 09/Feb/21 $$\int{e}^{\frac{{y}^{\mathrm{2}} }{\mathrm{2}}} {dy}=\sqrt{\frac{\pi}{\mathrm{2}}}\:{erfi}\left(\frac{{y}}{\:\sqrt{\mathrm{2}}}\right)+{C}…

Question Number 133470 by rs4089 last updated on 22/Feb/21 Answered by mr W last updated on 22/Feb/21 $$x=a\cos \theta$$$$y=b\sin \theta$$$$dV=-2\pi (2a-a\cos \theta )2ydx$$$$=\mathrm{4}\pi{a}\left(\mathrm{2}−\mathrm{cos}\:\theta\right){b}\mathrm{sin}\:\theta{a}\mathrm{sin}\:\theta{d}\theta \…

Question Number 67931 by mathmax by abdo last updated on 02/Sep/19 $$let{A}_n={\int }_0^{\frac{\pi }{4}}{x}^n{\{1+cosx+cos\left(2x\right)\}}^{2}dx$$$$findarelationofrecurrencebetwednthe{A}_n$$ Terms of Service Privacy…

Question Number 133452 by bagjagunawan last updated on 22/Feb/21 Answered by mnjuly1970 last updated on 22/Feb/21 $$\mathit{\varphi }\stackrel{x=2y-1}{=}{\int }_{\frac{1}{2}}^1\frac{ln(2-2y)ln\left(ln\left(2y\right)\right)}{2y}\left(2\right)dy$$$$=\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\:\mathrm{1}} \left({ln}\left(\mathrm{2}\right)+{ln}\left(\mathrm{1}−{y}\right)\right)\left({ln}\left(\mathrm{2}\right)+{ln}\left({y}\right)\right)\frac{{dy}}{{y}} \…

Question Number 67907 by A8;15: last updated on 02/Sep/19 Commented by mathmax by abdo last updated on 02/Sep/19 $$letI=\int \frac{dx}{x\sqrt{x^2+x-6}}$$$${x}^{\mathrm{2}} +{x}−\mathrm{6}=\mathrm{0}\rightarrow\Delta=\mathrm{1}−\mathrm{4}\left(−\mathrm{6}\right)\:=\mathrm{25}\:\Rightarrow{x}_{\mathrm{1}} =\frac{−\mathrm{1}+\mathrm{5}}{\mathrm{2}}=\mathrm{2}\:\:{and}\: \…