Category: Integration

Question Number 218662 by Nicholas666 last updated on 14/Apr/25 $$$$$$Prove:{\underset{0}{\int }}^{\mathrm{\infty }}\frac{sin\left(x\right)}{x}dx=\frac{\pi }{2}$$$$$$ Answered by SdC355 last updated on 14/Apr/25…

Question Number 218709 by Nicholas666 last updated on 14/Apr/25 $$$$$${\int }_0^{\pi /2}\frac{d\theta }{\sqrt{sin\theta +cos\theta }}$$$$$$ Answered by Nicholas666 last updated on 14/Apr/25…

Question Number 218626 by Nicholas666 last updated on 13/Apr/25 $$$$$$Provethatforallrealnumbersaandb$$$$witha<b,thefollowinginequalityholds;$$$$\left(\int_{{a}} ^{{b}} \mathrm{1}\:{dx}\right)^{\mathrm{3}} \leqslant\:\left({b}−{a}\right)\left(\int_{{a}} ^{{b}} \left({x}−{a}+\mathrm{1}\right)^{\mathrm{2}} {dx}\right)\left(\int_{{a}\:} ^{{b}} \frac{\mathrm{1}}{\left({a}−{x}+\mathrm{1}\right)^{\mathrm{3}} }{dx}\right)…

Question Number 218582 by Nicholas666 last updated on 12/Apr/25 $$$$$${\int }_0^{\mathrm{\infty }}\frac{cos\left(ax\right)-cos\left(bx\right)}{x^2}dx=\frac{\pi }{2}\mid b-a\mid$$$$$$ Answered by aleks041103 last updated on…

Question Number 218598 by Nicholas666 last updated on 12/Apr/25 $$$$$${\underset{0}{\int }}^{\mathrm{\infty }}\frac{\mathit{x}}{\mathit{s}\mathit{i}\mathit{n}\mathit{h}\left(\mathit{x}\right)}\mathit{l}\mathit{n}\left(\frac{\mathit{x}}{{\mathit{e}}^{\mathit{x}}-1}\right)\mathit{d}\mathit{x}$$$$$$ Terms of Service Privacy Policy Contact:…