- #1

transgalactic

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suppose that for every sub part [tex][\alpha ,\beta ]\subseteq [a,b][/tex]

we have[tex]\int_{\alpha}^{\beta}f(x)dx>0[/tex].

prove that f(x)>=0 for [tex] x\in[a,b] [/tex]

if its wrong give a contradicting example??

i don't have a clue from here to start or how to go.

from the given i can conclude that if the sum of all subsections gives us a positive result then

the total sum from a to b has to positive too.

when we solve an integral we take the anti derivative of f(x)

then subtract (beta substituted by x) with alpha substituted by x.

so if we get a positive result, then the value beta substituted by x is bigger.