Question Number 64334 by Chi Mes Try last updated on 16/Jul/19
$$\underset{{a}} {\overset{{b}} {\int}}\:\:\:\mid\:{f}\left({x}\right)\:\mid\:{dx}\:=\:\mathrm{0}\:\Rightarrow\:\underset{{a}} {\overset{{b}} {\int}}\:\:\left({f}\left({x}\right)\right)^{\mathrm{2}} \:{dx}\:=\:\mathrm{0} \\ $$
Commented by mr W last updated on 16/Jul/19
$${if}\:\underset{{a}} {\overset{{b}} {\int}}\:\:\:\mid\:{f}\left({x}\right)\:\mid\:{dx}\:=\:\mathrm{0} \\ $$$$\Rightarrow{f}\left({x}\right)=\mathrm{0} \\ $$$$\Rightarrow\underset{{a}} {\overset{{b}} {\int}}\:\:\left({f}\left({x}\right)\right)^{{n}} \:{dx}\:=\:\mathrm{0} \\ $$