Question Number 46853 by maxmathsup by imad last updated on 01/Nov/18 $${fnd}\:\:\int\:\:\:\:\:\:\frac{{dx}}{\mathrm{1}+{cos}\left({tx}\right)} \\ $$ Commented by maxmathsup by imad last updated on 01/Nov/18 $${let}\:{A}\left({t}\right)\:=\int\:\:\frac{{dx}}{\mathrm{1}+{cos}\left({tx}\right)}\:\Rightarrow{A}\left({t}\right)\:=_{{tx}={u}} \:\:\:\int\:\:\:\frac{\mathrm{1}}{\mathrm{1}+{cosu}}\:\frac{{du}}{{t}}…
Question Number 46850 by maxmathsup by imad last updated on 01/Nov/18 $${let}\:{a}^{\mathrm{2}} >{b}^{\mathrm{2}\:} +{c}^{\mathrm{2}} \:\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{d}\theta}{{a}+{bsin}\theta\:+{c}\:{cos}\theta} \\ $$ Commented by maxmathsup by imad last…
Question Number 46851 by maxmathsup by imad last updated on 01/Nov/18 $${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sint}}{{x}\:+{sint}}{dt}\:\:{withx}>\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{sint}}{\left({x}+{sint}\right)^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sint}}{\mathrm{2}+{sint}}{dt}\:{and}\:\int_{\mathrm{0}}…
Question Number 46849 by maxmathsup by imad last updated on 01/Nov/18 $$\left.{let}\:{A}_{{p}} =\sum_{{n}=\mathrm{1}} ^{\infty} \:{n}^{{p}} {x}^{{n}} \:\:\:\:{with}\:{p}\:{integr}\:.\:{and}\:{x}\:\in\right]−\mathrm{1},\mathrm{1}\left[\:.\right. \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{\mathrm{1}} ,{A}_{\mathrm{2}} \:{and}\:{A}_{\mathrm{3}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{a}\:{relation}\:{of}\:{recurrence}\:\:{betwen}\:{the}\:{A}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\sum_{{n}=\mathrm{1}}…
Question Number 46847 by maxmathsup by imad last updated on 01/Nov/18 $${calculate}\:\:\int\int_{\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:{and}\:\mathrm{1}\leqslant{y}\leqslant\mathrm{2}} \:\:{e}^{\frac{{x}}{{y}}} {dxdy} \\ $$ Commented by maxmathsup by imad last updated on 04/Nov/18…
Question Number 46848 by maxmathsup by imad last updated on 01/Nov/18 $${caculate}\:\:\int\int_{{D}} \:\:\left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right)\:{e}^{−{x}^{\mathrm{2}} \:−{y}^{\mathrm{2}} } {dxdy}\:\:{with} \\ $$$${D}\:=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:\:\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:\leqslant\mathrm{4}\right\} \\ $$…
Question Number 46846 by maxmathsup by imad last updated on 01/Nov/18 $${calculate}\:\int\int_{{D}} \:\:\:\:\frac{{x}+{y}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }}{dxdy}\:{with}\:{D}=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /{x}\geqslant\mathrm{0},{y}\geqslant\mathrm{0},{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} <\mathrm{1}\right\} \\ $$ Commented by maxmathsup by imad…
Question Number 112381 by M±th+et+s last updated on 07/Sep/20 $$\int{sin}\left({x}^{\mathrm{3}} \right)\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 46845 by maxmathsup by imad last updated on 01/Nov/18 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{e}^{−{x}} }{\mathrm{1}+{x}}\:{dx}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 177913 by infinityaction last updated on 11/Oct/22 $$\:\:\:\:\:\:\:\boldsymbol{\mathrm{if}}\:\:\boldsymbol{\mathrm{I}}_{\boldsymbol{\mathrm{n}}} =\int\boldsymbol{\mathrm{xsin}}^{\boldsymbol{\mathrm{n}}} \boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{dx}}\:\:\:\boldsymbol{\mathrm{and}}\:\: \\ $$$$\boldsymbol{\mathrm{I}}_{\boldsymbol{\mathrm{n}}} \:=\:−\frac{\boldsymbol{\mathrm{xsin}}^{\boldsymbol{\mathrm{n}}−\mathrm{1}} \boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{cosx}}\:}{\boldsymbol{\mathrm{n}}}\:+\frac{\boldsymbol{\mathrm{sin}}^{\boldsymbol{\mathrm{n}}} \boldsymbol{\mathrm{x}}\:}{\boldsymbol{\mathrm{n}}^{\mathrm{2}} }+\mathrm{f}\left(\mathrm{n}\right)\mathrm{I}_{\mathrm{n}−\mathrm{2}} \\ $$$$\:\:\:\mathrm{then}\:\:\mathrm{f}\left(\mathrm{n}\right)\:=\:? \\ $$ Terms of Service…