Category: Integration

Question Number 152492 by nadovic last updated on 28/Aug/21 $$\mathrm{A}\mathrm{particle}\mathrm{is}\mathrm{projected}\mathrm{upwards}\mathrm{with}$$$$\mathrm{a}\mathrm{velocity}\mathrm{of}96{ms}^{-1}.\mathrm{In}\mathrm{addition}\mathrm{to}$$$$\mathrm{being}\mathrm{subject}\mathrm{to}\mathrm{gravity},\mathrm{it}\mathrm{is}\mathrm{acted}\mathrm{on}$$$$\mathrm{by}\mathrm{a}\mathrm{retardation}\mathrm{of}16t,\mathrm{where}t\mathrm{is}\mathrm{the}$$$$\mathrm{time}\mathrm{from}\mathrm{the}\mathrm{start}\mathrm{of}\mathrm{the}\mathrm{motion}.$$$$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{greatest}\mathrm{height}\mathrm{attained}$$$$\mathrm{by}\mathrm{the}\mathrm{particle}?$$…

Question Number 152494 by mnjuly1970 last updated on 28/Aug/21 $$$$$$provethat::$$$$$$$$\mathrm{\Omega }:={\int }_0^{\mathrm{\infty }}\frac{e^{-x}.\ln \left(\frac{1}{x}\right)sin\left(x\right)}{x}dx=\frac{\pi }{8}(2\gamma +\ln \left(2\right))\dots \mathrm{<img\; draggable="false"\; role="img"\; class="emoji"\; alt="◼"\; src="https://s.w.org/images/core/emoji/15.1.0/svg/25fc.svg">}$$$$m.n$$$$$$…

Question Number 86955 by abdomathmax last updated on 01/Apr/20 $$find\int \frac{arctan\left(x\right)}{x}dx$$ Commented by Ar Brandon last updated on 01/Apr/20 $$Letf\left(a\right)=\int \frac{arctan\left(ax\right)}{x}dx$$$$\Rightarrow{f}\:'\:\left({a}\right)=\int\frac{{x}}{{x}}\centerdot\frac{\mathrm{1}}{\mathrm{1}+\left({ax}\right)^{\mathrm{2}} }{dx}=\int\frac{\mathrm{1}}{\mathrm{1}+\left({ax}\right)^{\mathrm{2}} }{dx}…

Question Number 152468 by talminator2856791 last updated on 28/Aug/21 $$$$$${\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\frac{\ln \left(\sqrt{x^4+1}\right)}{\sqrt{x^4+1}}dx$$$$$$ Answered by mindispower last updated…

Question Number 86914 by Chi Mes Try last updated on 01/Apr/20 Terms of Service Privacy Policy Contact: info@tinkutara.com