Menu Close

Category: Integration

prove-that-x-csch-x-2-x-2-pi-2-dx-pi-2-

Question Number 174896 by amin96 last updated on 14/Aug/22 $$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}} \\ $$$$\int_{−\infty} ^{\:\infty} \frac{\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{csch}}\left(\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\right)}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\pi^{\mathrm{2}} }\boldsymbol{\mathrm{dx}}=\pi−\mathrm{2} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

let-a-x-0-pi-2-dt-x-asin-2-t-2-find-a-exlicite-form-of-a-x-3-determine-1-x-and-a-1-4-find-the-vslue-of-0-pi-2-dt-2-3sin-2-t-5-find-0-pi-2-dt-x-asin-2-t-2-

Question Number 43823 by abdo.msup.com last updated on 15/Sep/18 $${let}\:\varphi\left({a},{x}\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{dt}}{{x}+{asin}^{\mathrm{2}} {t}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{a}\:{exlicite}\:{form}\:{of}\:\varphi\left({a},{x}\right) \\ $$$$\left.\mathrm{3}\right){determine}\:\varphi\left(\mathrm{1},{x}\right){and}\:\varphi\left({a},\mathrm{1}\right) \\ $$$$\left.\mathrm{4}\right){find}\:{the}\:{vslue}\:{of}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{dt}}{\mathrm{2}+\mathrm{3}{sin}^{\mathrm{2}} {t}} \\ $$$$\left.\mathrm{5}\right){find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…

let-I-0-dx-x-4-i-and-J-0-dx-x-4-i-1-find-values-of-I-and-J-2-calculate-I-J-3-calculate-0-dx-x-8-1-

Question Number 43808 by maxmathsup by imad last updated on 15/Sep/18 $${let}\:{I}\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{{x}^{\mathrm{4}} −{i}}\:{and}\:{J}\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{{x}^{\mathrm{4}} \:+{i}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:\:{values}\:{of}\:{I}\:{and}\:{J} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{I}\:+{J} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty}…

let-f-x-1-x-1-2-x-1-1-find-f-1-x-2-find-f-x-dx-3-find-f-1-x-dx-4-find-dx-f-1-x-

Question Number 43809 by maxmathsup by imad last updated on 15/Sep/18 $${let}\:{f}\left({x}\right)\:=\frac{\mathrm{1}−\sqrt{{x}−\mathrm{1}}}{\mathrm{2}+\sqrt{{x}−\mathrm{1}}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{f}^{−\mathrm{1}} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:\int\:{f}\left({x}\right){dx} \\ $$$$\left.\mathrm{3}\right)\:{find}\:\:\int\:\:{f}^{−\mathrm{1}} \left({x}\right){dx} \\ $$$$\left.\mathrm{4}\right)\:{find}\:\int\:\:\:\frac{{dx}}{{f}^{−\mathrm{1}} \left({x}\right)}\:. \\ $$…

Question-109342

Question Number 109342 by 150505R last updated on 22/Aug/20 Commented by maths mind last updated on 23/Aug/20 $${x}={tg}\left({t}\right),{dx}=\left(\mathrm{1}+{tg}^{\mathrm{2}} \left({t}\right)\right){dt} \\ $$$$=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left(\frac{{cos}^{\mathrm{2}} \left({t}\right)−{sin}^{\mathrm{2}} \left({t}\right)}{{sin}\left({t}\right){cos}\left({t}\right)}\right).{dt}…

Question-43731

Question Number 43731 by Meritguide1234 last updated on 14/Sep/18 Answered by MJS last updated on 14/Sep/18 $$\int\left(\frac{{x}^{\mathrm{2}} −\mathrm{3}{x}+\frac{\mathrm{1}}{\mathrm{3}}}{{x}^{\mathrm{3}} −{x}+\mathrm{1}}\right)^{\mathrm{2}} {dx}=\frac{\mathrm{1}}{\mathrm{9}}\int\frac{\left(\mathrm{3}{x}^{\mathrm{2}} +\mathrm{9}{x}+\mathrm{1}\right)^{\mathrm{2}} }{\left({x}^{\mathrm{3}} −{x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\…