Question Number 156369 by tabata last updated on 10/Oct/21
$${solve}\:{by}\:{betta}\:{function}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} {sin}^{\mathrm{5}} \left({z}\right)\:{dz} \\ $$
Commented by tabata last updated on 10/Oct/21
$$???????? \\ $$
Commented by aliyn last updated on 10/Oct/21
$$?????? \\ $$
Answered by Mathspace last updated on 11/Oct/21
$$\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:{sin}^{\mathrm{5}} {x}\:{dx} \\ $$$$ \\ $$$$=\int_{\mathrm{0}} ^{\pi} \:{sin}^{\mathrm{5}} {x}\:{dx}\:+\int_{\pi} ^{\mathrm{2}\pi\:} {sin}^{\mathrm{5}} {x}\:{dx}\left(\rightarrow{x}=\pi+{u}\right) \\ $$$$=\int_{\mathrm{0}} ^{\pi\:} {sin}^{\mathrm{5}} {xdx}+\int_{\mathrm{0}} ^{\pi} \left(−{sin}^{\mathrm{5}} {u}\right){du} \\ $$$$=\mathrm{0}\:\:\:\:\:\left({no}\:{need}\:{for}\:{betta}...!\right) \\ $$$$ \\ $$$$ \\ $$