Question Number 162417 by HongKing last updated on 29/Dec/21
$$\mathrm{Prove} \\ $$$$\underset{\:\mathrm{0}} {\overset{\:\frac{\boldsymbol{\pi}}{\mathrm{2}}} {\int}}\:\mathrm{sin}^{\mathrm{8}} \left(\mathrm{x}\right)\:+\:\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\mathrm{sin}^{-\mathrm{1}} \:\left(\sqrt[{\mathrm{8}}]{\mathrm{x}}\right)\:\geqslant\:\frac{\pi}{\mathrm{2}} \\ $$
Commented by mr W last updated on 29/Dec/21
$$``\geqslant``\:{should}\:{be}\:``=''. \\ $$
Commented by HongKing last updated on 29/Dec/21
$$\mathrm{yes}\:\mathrm{my}\:\mathrm{dear}\:\mathrm{Sir} \\ $$
Commented by mr W last updated on 29/Dec/21
$${see}\:{Q}\mathrm{162471} \\ $$
Commented by HongKing last updated on 31/Dec/21
$$\mathrm{cool}\:\mathrm{my}\:\mathrm{dear}\:\mathrm{Sir}\:\mathrm{thank}\:\mathrm{you}\:\mathrm{so}\:\mathrm{much} \\ $$