Category: Integration

Question Number 1673 by 123456 last updated on 31/Aug/15 $$\omega \in \mathbb{R},\omega >0$$$$0<\alpha <\beta$$$$f_m(\alpha ,\beta )=\frac{\omega }{\beta -\alpha }\underset{\alpha /\omega }{\stackrel{\beta /\omega }{\int }}\sin \left(\omega t\right)dt$$$$f_r(\alpha ,\beta )=\sqrt{\frac{\omega }{\beta -\alpha }\underset{\alpha /\omega }{\stackrel{\beta /\omega }{\int }}{\sin }^2\left(\omega t\right)dt}$$$${f}_{{m}}…

Question Number 132729 by mnjuly1970 last updated on 16/Feb/21 $$\dots .advancedcalculus\dots$$$$evaluate:$$$$\mathit{\varphi }={\int }_0^{\mathrm{\infty }}{xe}^{-2x}ln\left(x\right)dx=???$$$$$$ Answered by Olaf last…

Question Number 1643 by 112358 last updated on 28/Aug/15 $$Calculate$$$$I(a,b)={\int }_0^1{t}^a{(1-t)}^{b}dt$$$$giventhatI(a,b)=\frac{b}{a+1}I(a+1,b-1)$$$$(a>0,b>0).Usethefactthat$$$$I(a,b)=I(a+1,b)+I(a,b+1)$$$${and}\:{I}\left({a},{b}\right)={I}\left({b},{a}\right)\: \…

Question Number 1625 by 112358 last updated on 27/Aug/15 $$y\left(x\right)=\frac{1}{x-a}{\int }_a^x\sqrt{t+\sqrt{t+\sqrt{t+\sqrt{t+\sqrt{t+\dots }}}}}dt$$$$x\ne a,a>0,y\left(x\right)>0.$$$$Findy\left(2a\right).$$ Answered by Rasheed Soomro last updated on…

Question Number 67153 by mhmd last updated on 23/Aug/19 $$find\int (v^3-2)/(v^4+v)dv$$ Answered by mhmd last updated on 23/Aug/19 $$$$ Answered…