if we have that:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \int_{a}^{b}dxf(x) - \int_{a}^{b}dxg(x)= \int_{a}^{b}dx(f(x)-g(x)) [/tex]

where the integral over (a,b) of f(x) and g(x) exist separately then my question is if

[tex] \int_{a}^{b}dx(f(x)-g(x)) =0 [/tex] then

does this imply necessarily that [tex] f(x)=g(x)+h'(x) [/tex]

where h(a)=h(b)=0 and its derivative is 0 almost everywhere on the interval (a,b)

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# Integral equality paradox?

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