Category: Integration

Question Number 50052 by cesar.marval.larez@gmail.com last updated on 13/Dec/18 Commented by maxmathsup by imad last updated on 13/Dec/18 $${let}\:{I}\:=\:\int\:\:\:\frac{{x}^{\mathrm{2}\:} +\mathrm{2}{x}}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }{dx}\:{changement}\:{x}+\mathrm{1}\:={t}\:{give} \\ $$$${I}\:=\:\int\:\:\frac{\left({t}−\mathrm{1}\right)^{\mathrm{2}} \:+\mathrm{2}\left({t}−\mathrm{1}\right)}{{t}^{\mathrm{2}} }{dt}\:=\int\:\frac{{t}^{\mathrm{2}}…

Question Number 50007 by Joel578 last updated on 13/Dec/18 $$\mathrm{For}\:{a}\:<\:{x}\:<\:{b},\:\mathrm{find}\: \\ $$$$\underset{{a}} {\overset{{b}} {\int}}\:\sqrt{{x}−{a}}\:.\:\sqrt{{b}−{x}}\:{dx} \\ $$ Commented by Abdo msup. last updated on 13/Dec/18 $${changement}\:\sqrt{{x}−{a}}={t}\:{give}\:{x}−{a}={t}^{\mathrm{2}}…

Question Number 115533 by mnjuly1970 last updated on 26/Sep/20 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 115507 by mnjuly1970 last updated on 26/Sep/20 $$\:\:\:\:\:\:\:\:\:\:\:….\:\:\:…{matematical}\:{analysis}…\:\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:{prove}\:{that}\:::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{a}>\mathrm{0}\:::\:\:\:\begin{bmatrix}{{i}\::\:\:\int_{\mathrm{0}\:} ^{\:\infty} \frac{{sin}^{\mathrm{2}} \left({ax}\right)}{{x}^{\frac{\mathrm{3}}{\mathrm{2}}} }\:{dx}=\:\sqrt{\pi{a}}}\\{{ii}:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}^{\mathrm{3}} \left({ax}\right)}{\:\sqrt{{x}}}\:{dx}\:=\:\frac{−\mathrm{1}+\mathrm{3}\sqrt{\mathrm{3}\:}}{\mathrm{4}}\:\sqrt{\frac{\pi}{\mathrm{6}{a}}\:\:}\:}\end{bmatrix} \\ $$$$\:\:\:\:\:…

Question Number 49968 by maxmathsup by imad last updated on 12/Dec/18 $${find}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{{t}\:{arctan}\left({xt}\right)}{\mathrm{1}+{t}^{\mathrm{4}} }\:{dt} \\ $$ Commented by mathmax by abdo last updated on…