Question Number 62833 by aliesam last updated on 25/Jun/19 $$\int\frac{{cos}\left({x}\right)}{{x}}\:{dx} \\ $$$$ \\ $$$$\int\sqrt{{sin}\left({x}\right)\:}\:{dx} \\ $$$$ \\ $$$$\int\sqrt{\mathrm{1}−{k}^{\mathrm{2}} {sin}^{\mathrm{2}} \left({x}\right)}\:{dx}\:\:\:\:\:\:{k}:{constant} \\ $$ Commented by mathmax…
Question Number 128369 by I want to learn more last updated on 06/Jan/21 $$\mathrm{If}\:\:\:\mathrm{u}_{\mathrm{1}} \:\:+\:\:\mathrm{u}_{\mathrm{2}} \:\:+\:\:\mathrm{u}_{\mathrm{3}} \:\:+\:\:…\:\:+\:\:\mathrm{u}_{\mathrm{n}} \:\:\:=\:\:\:\mathrm{2n}^{\mathrm{2}} \:\:+\:\:\mathrm{n}\:\:\:\mathrm{is}\:\mathrm{an}\:\mathrm{AP}. \\ $$$$\mathrm{Find}\:\:\:\:\:\:\:\:\mathrm{u}_{\mathrm{1}} \:\:+\:\:\mathrm{u}_{\mathrm{2}} \:\:+\:\:\mathrm{u}_{\mathrm{3}} \:\:+\:\:…\:\:+\:\:\mathrm{u}_{\mathrm{2n}\:\:−\:\:\mathrm{2}} \:\:+\:\:\mathrm{u}_{\mathrm{2n}\:\:−\:\:\mathrm{1}}…
Question Number 62828 by mathmax by abdo last updated on 25/Jun/19 $${let}\:{U}_{{n}} =\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{cos}\left({ch}\left({nx}\right)\right)}{\left(\mathrm{3}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{n}\:{U}_{{n}} \:\:\:\:\:{and}\:{lim}_{{n}\rightarrow+\infty} \:{n}^{\mathrm{2}}…
Question Number 62826 by Cheyboy last updated on 25/Jun/19 Commented by mathmax by abdo last updated on 25/Jun/19 $$\left.{b}\right)\:{I}\:=\int_{\mathrm{0}} ^{\pi} \:\:\frac{{sin}\theta}{\:\sqrt{\pi−\theta}}\:\:{changement}\sqrt{\pi−\theta}\:={x}\:{give}\:{I}\:=\int_{\sqrt{\pi}} ^{\mathrm{0}} \:\frac{{sin}\left(\pi−{x}^{\mathrm{2}} \right)}{{x}}\:\left(−\mathrm{2}{x}\right){dx} \\…
Question Number 128361 by DomaPeti last updated on 06/Jan/21 $${f}\left({x}\right)= \\ $$$$\frac{{R}}{\:\sqrt{\mathrm{1}−{M}^{\mathrm{2}} {sin}^{\mathrm{2}} \left({atan}\left({N}\centerdot{sin}\left({x}+{c}\right)\right)\right)}} \\ $$$${g}\left({x}\right)={acos}\left({A}\centerdot{sin}\left({atan}\left({N}\centerdot{sin}\left({x}+{c}\right)\right)\right)+\right. \\ $$$$\left.{B}\centerdot{cos}\left({atan}\left({N}\centerdot{sin}\left({x}+{c}\right)\right)\right)\centerdot{cos}\left({D}−{x}\right)\right) \\ $$$$\int\left({f}\left({x}\right)\centerdot{g}\left({x}\right)'\right)={L}\left({x}\right) \\ $$$${L}\left({x}\right)=? \\ $$$$ \\…
Question Number 62821 by ajfour last updated on 25/Jun/19 Commented by ajfour last updated on 25/Jun/19 $${If}\:{the}\:{right}\:{circular}\:{cone}\:{contains} \\ $$$${half}\:{the}\:{spherical}\:{volume}\:{within} \\ $$$${its}\:{lateral}\:{surface},\:{find}\:\boldsymbol{\alpha}. \\ $$ Answered by…
Question Number 62815 by mathmax by abdo last updated on 25/Jun/19 $${developp}\:{at}\:{fourier}\:{serie}\:{f}\left({x}\right)\:={cos}\left({tx}\right)\:\:,\mathrm{2}\pi\:{periodic}\:{even}\:. \\ $$ Commented by mathmax by abdo last updated on 28/Jun/19 $${f}\:{is}\:{even}\:\Rightarrow{f}\left({x}\right)\:=\frac{{a}_{\mathrm{0}} }{\mathrm{2}}\:+\sum_{{n}=\mathrm{1}}…
Question Number 62814 by Cheyboy last updated on 25/Jun/19 Commented by Cheyboy last updated on 25/Jun/19 $${Please}\:{help}\:{me}\:{with}\:{these}\:{question} \\ $$ Commented by mathmax by abdo last…
Question Number 62813 by mathmax by abdo last updated on 25/Jun/19 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−\left({t}^{\mathrm{2}} \:+\frac{\mathrm{1}}{{t}^{\mathrm{2}} }\right)} {dt} \\ $$$${study}\:{first}\:{the}\:{convergence}\:. \\ $$ Terms of Service Privacy…
Question Number 128349 by mathocean1 last updated on 06/Jan/21 $${function}\:{g}\:{is}\:{defined}\:{in}\:\left[\mathrm{0};\frac{\pi}{\mathrm{4}}\right] \\ $$$${by}\:{g}\left({x}\right)=\frac{{sinx}}{{cos}^{\mathrm{3}} {x}}. \\ $$$$\mathrm{1}.\:{Determinate}\:{a};{b}\:\in\mathbb{R}\:{such}\:{that} \\ $$$${g}'\left({x}\right)=\frac{{a}}{{cos}^{\mathrm{4}} {x}}\:+\:\frac{{b}}{{cos}^{\mathrm{2}} {x}}. \\ $$$$\mathrm{2}.{Deduct}\:{the}\:{primitive}\:{G}\:{of}\:{the}\: \\ $$$${function}\:{t}\left({x}\right)=\frac{\mathrm{1}}{{cos}^{\mathrm{4}} {x}}\:\:{such}\:{that} \\…