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a-b-f-x-dx-0-a-b-f-x-2-dx-0-




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

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