Question Number 202636 by ibroclex_adex last updated on 30/Dec/23 $$\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\:^{\mathrm{3}} \sqrt{\mathrm{4}^{\mathrm{5}−\mathrm{x}} }}{\int_{\mathrm{4}} ^{\mathrm{6}} \left(\mathrm{x}−\mathrm{1}\right){dx}}\:=\:\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2x}−\mathrm{1}} }\:,\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underline{\mathrm{Solution}}…
Question Number 202592 by Calculusboy last updated on 30/Dec/23 $$\:\boldsymbol{{If}}\:\:\boldsymbol{{I}}_{\boldsymbol{{n}}} \:\boldsymbol{{denotes}}\:\int\boldsymbol{{z}}^{\boldsymbol{{n}}} \boldsymbol{{e}}^{\frac{\mathrm{1}}{\boldsymbol{{z}}}} \boldsymbol{{dz}},\:\boldsymbol{{then}}\:\boldsymbol{{show}}\:\boldsymbol{{that}} \\ $$$$\left(\boldsymbol{{n}}+\mathrm{1}\right)!\boldsymbol{{I}}_{\boldsymbol{{n}}} =\boldsymbol{{I}}_{\mathrm{0}} +\boldsymbol{{e}}^{\frac{\mathrm{1}}{\boldsymbol{{z}}}} \left(\mathrm{1}\centerdot!\boldsymbol{{z}}^{\mathrm{2}} +\mathrm{2}\centerdot!\boldsymbol{{z}}^{\mathrm{3}} +\centerdot\centerdot\centerdot+\boldsymbol{{n}}!\centerdot\boldsymbol{{z}}^{\boldsymbol{{n}}+\mathrm{1}} \right) \\ $$$$ \\ $$…
Question Number 202543 by mr W last updated on 29/Dec/23 Commented by mr W last updated on 29/Dec/23 $${unsolved}\:{old}\:{question}\:{Q}\mathrm{201806} \\ $$ Answered by mr W…
Question Number 202522 by mou0113 last updated on 28/Dec/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 202490 by Calculusboy last updated on 27/Dec/23 Commented by aleks041103 last updated on 27/Dec/23 $${is}\:\left\{{x}\right\}\:{the}\:{whole}\:{part}\:{or}\:{the}\:{fractional}\:{part}? \\ $$ Commented by Calculusboy last updated on…
Question Number 202485 by Calculusboy last updated on 27/Dec/23 Commented by MathematicalUser2357 last updated on 28/Dec/23 $$\mathrm{Can}'\mathrm{t}\:\mathrm{integrate}\:\mathrm{in}\:\mathrm{range}\:\left[−\infty,\:\infty\right] \\ $$ Commented by TheHoneyCat last updated on…
Question Number 202448 by Calculusboy last updated on 26/Dec/23 Answered by professorleiciano last updated on 27/Dec/23 $${Nao}\:{tem}\:{antiderivada}\:{elementar}. \\ $$ Answered by MathematicalUser2357 last updated on…
Question Number 202418 by MathematicalUser2357 last updated on 26/Dec/23 $$\mathrm{Hard}\:\mathrm{integral} \\ $$$$\int\int\int\int\int\int\int\int\int\begin{vmatrix}{{a}}&{{b}}&{{c}}\\{{f}}&{{g}}&{{h}}\\{{j}}&{{k}}&{{l}}\end{vmatrix}{dl}\:{dk}\:{dj}\:{dh}\:{dg}\:{df}\:{dc}\:{db}\:{da}= \\ $$ Answered by Frix last updated on 26/Dec/23 $$\mathrm{Not}\:\mathrm{hard}\:\mathrm{at}\:\mathrm{all} \\ $$$$=\frac{{abcfghjkl}}{\mathrm{8}}\left({a}\left({gl}−{hk}\right)−{b}\left({fl}−{hj}\right)+{c}\left({fk}−{gj}\right)\right) \\…
Question Number 202415 by MathematicalUser2357 last updated on 26/Dec/23 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\int{g}'\left({x}\right){f}'\left({g}\left({x}\right)\right){dx}\:\mathrm{is}… \\ $$ Answered by cortano12 last updated on 26/Dec/23 $$\:\mathrm{let}\:\mathrm{u}=\mathrm{g}\left(\mathrm{x}\right)\Rightarrow\mathrm{du}=\:\mathrm{g}'\left(\mathrm{x}\right)\:\mathrm{dx} \\ $$$$\:\mathrm{I}=\:\int\:\mathrm{g}'\left(\mathrm{x}\right)\:\mathrm{f}\:'\left(\mathrm{g}\left(\mathrm{x}\right)\right)\:\mathrm{dx}\: \\ $$$$\:\:\:=\:\int\:\mathrm{f}\:'\left(\mathrm{u}\right)\:\mathrm{du}=\:\int\:\frac{\mathrm{df}\left(\mathrm{u}\right)}{\mathrm{du}}.\:\mathrm{du} \\…
Question Number 202406 by mou0113 last updated on 26/Dec/23 Answered by witcher3 last updated on 26/Dec/23 $$\mathrm{f}\left(\mathrm{s}\right)=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{t}^{\mathrm{s}} }{\left(\mathrm{1}+\mathrm{t}^{\mathrm{2}} \right)^{\mathrm{2}} }\mathrm{dt}\Rightarrow\mathrm{f}'\left(\mathrm{0}\right)=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{ln}\left(\mathrm{x}\right)}{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{2}}…