Question Number 74040 by Learner-123 last updated on 18/Nov/19 $${Find}\:{orthogonal}\:{trajectories}\:{of}\:{the} \\ $$$${curves}:\:\left({x}−{c}\right)^{\mathrm{2}} +{y}^{\mathrm{2}} ={c}^{\mathrm{2}} . \\ $$ Commented by Learner-123 last updated on 18/Nov/19 $${please}\:{help}……
Question Number 74037 by akshaypalsra8@gmail.com last updated on 18/Nov/19 $$\int_{\mathrm{0}^{} } ^{\Pi/\mathrm{2}} {x}\mathrm{cos}^{{n}} {xdx}\:\:\:{by}\:{reduction}\:{formula} \\ $$ Answered by mind is power last updated on 18/Nov/19…
Question Number 8490 by fernandodantas1996 last updated on 14/Oct/16 $${show}\:{thats}\:{true}: \\ $$$$\int_{−\infty} ^{+\infty} {e}^{−{x}^{\mathrm{2}} } =\:\sqrt{\pi} \\ $$ Commented by prakash jain last updated on…
Question Number 139556 by mnjuly1970 last updated on 28/Apr/21 $$\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:……..\:{advanced}\:…\:…\:…\:{calculus}…….. \\ $$$$\:\:\:\Phi=\:{lim}_{{n}\rightarrow\infty} \left\{\int_{\mathrm{1}} ^{\:{n}} \frac{{x}}{\left[{x}\right]^{\mathrm{2}} }\:{dx}\:−\psi\left({n}+\mathrm{1}\right)\right\}=? \\ $$$$\:\:\:\:{solution}: \\ $$$$\:\:\:\:\:\Phi_{{n}} =\int_{\mathrm{1}} ^{\:{n}} \frac{{x}}{\left[{x}\right]^{\mathrm{2}}…
Question Number 139524 by mnjuly1970 last updated on 28/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:……{advanced}\:\:{calculus}….. \\ $$$$\:\:\:\:\:\:\:\:\:{prove}\:\:{that}: \\ $$$$\:{i}::\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \left(\frac{\mathrm{1}}{\mathrm{2}}{e}^{−\mathrm{2}{x}} −\frac{\mathrm{1}}{\mathrm{1}+{e}^{{x}} }\right)\frac{\mathrm{1}}{{x}}\:{dx}={log}\left(\frac{\mathrm{1}}{\:\sqrt{\pi}}\:\right) \\ $$$$\:{ii}::\int_{\mathrm{0}} ^{\:\infty} \left(\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{1}+{e}^{−{x}} }\right)\frac{{e}^{−\mathrm{2}{x}} }{{x}}{dx}={log}\left(\frac{\sqrt{\pi}}{\mathrm{2}}\right) \\…
Question Number 139476 by aliibrahim1 last updated on 27/Apr/21 Answered by qaz last updated on 27/Apr/21 $${I}=\int\frac{{dx}}{{x}\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)…\left({x}+{n}\right)} \\ $$$${f}\left({x}\right)=\frac{\mathrm{1}}{{x}\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)…\left({x}+{n}\right)}=\frac{{A}_{\mathrm{0}} }{{x}}+\frac{{A}_{\mathrm{1}} }{{x}+\mathrm{1}}+\frac{{A}_{\mathrm{2}} }{{x}+\mathrm{2}}+…+\frac{{A}_{{n}} }{{x}+{n}} \\ $$$${A}_{\mathrm{0}}…
Question Number 139478 by mnjuly1970 last updated on 27/Apr/21 $$\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:………\:{nice}\:…\:…\:…\:{calculus}…….. \\ $$$$\:\:\:\:\:\:\Phi:=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left(\frac{\mathrm{1}+{x}}{\mathrm{2}}\right)}{{x}^{\mathrm{2}} −\mathrm{1}}{dx}=\frac{\pi^{\mathrm{2}} }{\mathrm{24}} \\ $$$$\:\:\:\:\:\:\:{NOTE}\:::\:{li}_{\mathrm{2}} \left({z}\right)+{li}_{\mathrm{2}} \left(\mathrm{1}−{z}\right)=\frac{\pi^{\mathrm{2}} }{\mathrm{6}}−{ln}\left({z}\right){ln}\left(\mathrm{1}−{z}\right) \\ $$$$\:\:\:\:\:\:\:\:\:{Hence}\:::\:\:{li}_{\mathrm{2}}…
Question Number 139454 by aliibrahim1 last updated on 27/Apr/21 Answered by Dwaipayan Shikari last updated on 27/Apr/21 $$\int{x}^{\mathrm{2}} \frac{{tan}^{−\mathrm{1}} {x}}{{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$$$=\int{tan}^{−\mathrm{1}} \left({x}\right)−\int\frac{{tan}^{−\mathrm{1}} \left({x}\right)}{{x}^{\mathrm{2}}…
Question Number 139445 by aliibrahim1 last updated on 27/Apr/21 Answered by mr W last updated on 27/Apr/21 $${u}={xy} \\ $$$$\frac{{du}}{{dx}}={x}\frac{{dy}}{{dx}}+{y} \\ $$$$\frac{{du}}{{dx}}+\mathrm{3}{u}^{\mathrm{2}} =\mathrm{0} \\ $$$$−\frac{{du}}{{u}^{\mathrm{2}}…
Question Number 8375 by tawakalitu last updated on 09/Oct/16 $$\mathrm{Evaluate}\::\:\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \sqrt{\mathrm{1}\:−\:\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx} \\ $$$$\mathrm{By}\:\mathrm{direct}\:\mathrm{integration}\:\mathrm{and}\:\mathrm{by}\:\mathrm{expanding} \\ $$$$\mathrm{as}\:\mathrm{a}\:\mathrm{power}\:\mathrm{series}. \\ $$ Terms of Service Privacy Policy Contact:…