Question Number 131167 by 676597498 last updated on 02/Feb/21 Answered by SEKRET last updated on 02/Feb/21 $$\boldsymbol{\mathrm{U}}_{\boldsymbol{\mathrm{n}}} =\left(\mathrm{1}+\frac{\mathrm{1}}{\boldsymbol{\mathrm{n}}^{\mathrm{2}} }\right)\left(\mathrm{1}+\frac{\mathrm{2}}{\boldsymbol{\mathrm{n}}^{\mathrm{2}} }\right)….\left(\mathrm{1}+\frac{\boldsymbol{\mathrm{n}}}{\boldsymbol{\mathrm{n}}^{\mathrm{2}} }\right) \\ $$$$\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{U}}_{\boldsymbol{\mathrm{n}}} \right)=\:\boldsymbol{\mathrm{ln}}\left(\mathrm{1}+\frac{\mathrm{1}}{\boldsymbol{\mathrm{n}}^{\mathrm{2}} }\right)+\boldsymbol{\mathrm{ln}}\left(\mathrm{1}+\frac{\mathrm{2}}{\:\:\boldsymbol{\mathrm{n}}^{\mathrm{2}}…
Question Number 131146 by EDWIN88 last updated on 02/Feb/21 $${Given}\:{f}\left({x}\right)={f}\left({x}+\mathrm{6}\right)\:\forall{x}\in\mathbb{R} \\ $$$${If}\:\int_{−\mathrm{2}} ^{\:\mathrm{2}} {f}\left({x}\right){dx}=−\mathrm{2}\:{and}\:\int_{−\mathrm{2}} ^{\:\mathrm{4}} {f}\left({x}\right){dx}=\mathrm{2} \\ $$$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{4}} ^{\:\mathrm{10}} {f}\left({x}\right){dx}. \\ $$ Commented by EDWIN88…
Question Number 131147 by EDWIN88 last updated on 02/Feb/21 $$\:\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{1}}{\mathrm{1}+\sqrt{{x}−{x}^{\mathrm{3}} }}\:{dx}\:=?\: \\ $$ Commented by EDWIN88 last updated on 02/Feb/21 $$\:\sqrt{{x}−{x}^{\mathrm{3}} }\:=\:{w}−\mathrm{1}\:\Rightarrow{x}−{x}^{\mathrm{3}}…
Question Number 131138 by liberty last updated on 02/Feb/21 $$\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{arctan}\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{2}}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{2}}}\:\mathrm{dx}\:=? \\ $$ Answered by EDWIN88 last updated on 02/Feb/21 $$=\frac{\mathrm{5}\pi^{\mathrm{2}}…
Question Number 131135 by LYKA last updated on 01/Feb/21 Commented by LYKA last updated on 01/Feb/21 $${if}\:{anyone}\:{knows}\:{this}\:{question}\: \\ $$$${please}\:{help}\:{me} \\ $$ Terms of Service Privacy…
Question Number 53 by surabhi last updated on 25/Jan/15 $$\mathrm{Evaluate}\:\int_{\mathrm{1}} ^{\mathrm{4}} \frac{\left({x}^{\mathrm{2}} +{x}\right)}{\:\sqrt{\mathrm{2}{x}+\mathrm{1}}}{dx} \\ $$ Answered by surabhi last updated on 04/Nov/14 $$\left[\left({x}^{\mathrm{2}} +{x}\right)\centerdot\sqrt{\mathrm{2}{x}+\mathrm{1}}\right]_{\mathrm{2}} ^{\mathrm{4}}…
Question Number 51 by surabhi last updated on 25/Jan/15 $$\mathrm{Evaluate}\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}} {x}\mathrm{cos}\:{x}\:{dx} \\ $$ Answered by surabhi last updated on 04/Nov/14 $$\int_{\mathrm{0}} ^{\pi/\mathrm{2}} {x}\mathrm{cos}\:{x}\:{dx}=\left[{x}\mathrm{sin}\:{x}\right]_{\mathrm{0}} ^{\pi/\mathrm{2}}…
Question Number 46 by surabhi last updated on 25/Jan/15 $$\int\left(\mathrm{log}\:{x}\right)^{\mathrm{2}} {dx} \\ $$ Answered by surabhi last updated on 04/Nov/14 $$\int\left(\mathrm{log}\:{x}\right)^{\mathrm{2}} {dx}=\int\mid\left(\mathrm{log}\:{x}\right)^{\mathrm{2}} \centerdot\mathrm{1}\mid{dx} \\ $$$$=\left(\mathrm{log}\:{x}\right)^{\mathrm{2}}…
Question Number 48 by surabhi last updated on 25/Jan/15 $$\mathrm{Evaluate}\:\:\:\int\sqrt{\mathrm{3}−\mathrm{2}{x}−\mathrm{2}{x}^{\mathrm{2}} \:}{dx}. \\ $$ Answered by surabhi last updated on 04/Nov/14 $$\int\sqrt{\mathrm{3}−\mathrm{2}{x}−\mathrm{2}{x}^{\mathrm{2}} }\:{dx} \\ $$$$=\sqrt{\mathrm{2}}\:\centerdot\:\int\sqrt{\left(\frac{\mathrm{3}}{\mathrm{2}}−{x}−{x}^{\mathrm{2}} \right)}\:{dx}…
Question Number 50 by surabhi last updated on 25/Jan/15 $$\mathrm{Evaluate}\:\:\:\int\left({x}+\mathrm{1}\right)\sqrt{\mathrm{1}−{x}−{x}^{\mathrm{2}} }{dx}. \\ $$ Commented by 123456 last updated on 13/Dec/14 $$\mathrm{tente}?\mathrm{completar}\:\mathrm{quadrados}\:\mathrm{e}\:\mathrm{fca}\:\mathrm{uma}\:\mathrm{substutuico} \\ $$ Answered by…