Menu Close

Category: Integration

find-dx-1-cos-x-cos-2x-

Question Number 47059 by maxmathsup by imad last updated on 04/Nov/18 $$\:{find}\:\int\:\:\frac{{dx}}{\mathrm{1}+{cos}\:{x}\:+{cos}\left(\mathrm{2}{x}\right)} \\ $$ Commented by maxmathsup by imad last updated on 06/Nov/18 $${let}\:{A}\:=\int\:\:\:\frac{{dx}}{\mathrm{1}+{cosx}\:+{cos}\left(\mathrm{2}{x}\right)}\:=\:\int\:\:\frac{{dx}}{\mathrm{1}+{cos}\left({x}\right)+\mathrm{2}{cos}^{\mathrm{2}} {x}−\mathrm{1}}…

let-f-x-0-1-dt-2-ch-xt-1-find-a-explicit-form-of-f-x-2-calculate-g-x-0-1-tsh-xt-2-ch-xt-2-dt-3-find-the-value-of-0-1-dt-2-ch-3t-and-0-1-tsh-3t-

Question Number 47060 by maxmathsup by imad last updated on 04/Nov/18 $${let}\:{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{dt}}{\mathrm{2}+{ch}\left({xt}\right)} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{g}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{tsh}\left({xt}\right)}{\left(\mathrm{2}+{ch}\left({xt}\right)\right)^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{\mathrm{2}+{ch}\left(\mathrm{3}{t}\right)}\:{and}\:\:\int_{\mathrm{0}}…

calculus-Please-Evaluate-0-pi-2-x-sin-x-2-dx-M-N-july-1970-

Question Number 112579 by mnjuly1970 last updated on 08/Sep/20 $$\:\:\:\:\:\:\:\:….\:{calculus}\:…. \\ $$$$\mathscr{P}{lease}\:\:\mathscr{E}{valuate}\:::: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \left(\frac{{x}}{{sin}\left({x}\right)}\right)^{\mathrm{2}} {dx}\:=???\:\:\:\:\:\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathscr{M}.\mathscr{N}.{july}\:\mathrm{1970}# \\ $$$$\:…

find-x-2-x-1-dx-

Question Number 47018 by maxmathsup by imad last updated on 03/Nov/18 $${find}\:\int\:\sqrt{{x}+\mathrm{2}−\sqrt{{x}−\mathrm{1}}}{dx} \\ $$ Commented by maxmathsup by imad last updated on 04/Nov/18 $${let}\:{A}\:=\:\int\sqrt{{x}+\mathrm{2}−\sqrt{{x}−\mathrm{1}}}{dx}\:\:{changement}\:\sqrt{{x}−\mathrm{1}}={t}\:{give} \\…

sin-2x-1-cos-2-x-dx-

Question Number 112481 by bemath last updated on 08/Sep/20 $$\:\int\:\frac{\mathrm{sin}\:\mathrm{2x}}{\:\sqrt{\mathrm{1}+\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}}}\:\mathrm{dx}\: \\ $$ Answered by john santu last updated on 08/Sep/20 $$\:\:\int\:\frac{\mathrm{2sin}\:{x}\:\mathrm{cos}\:{x}}{\:\sqrt{\mathrm{1}+\mathrm{cos}\:^{\mathrm{2}} {x}}}\:{dx}\:=\:\int−\:\frac{\mathrm{2}{u}\:{du}}{\:\sqrt{\mathrm{1}+{u}^{\mathrm{2}} }} \\…