Prove that if f is continuous , and f=0 , then the integral of f is greater than or equal to zero for n-spaces. Refer to the image below . Thanks.

Question

Prove that if f is continuous , and f>=0 , then the integral of f is greater than or equal to zero for n-spaces. Refer to the image below . Thanks.

anonymous · Answer

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anonymous · Answer

@SithsAndGiggles  Any help getting started would be appreciated mate , I believe the only way to go about this is to use the definition of the definite integral? Cheers.

p0sitr0n · Answer

possibly could use a trick from Analysis I and feed f(xi) a sequence that always makes f stay positive. then argue that f(x_n) is still always positive. then put your Riemann integral definition there and basically show that at all point, you can either reconstruct or keep the same x_n such that your integral will stay positive. Then prove by induction on n that if the first integral is positive, then all of them are positive

anonymous · Answer

@P0sitr0n care to elaborate on that a bit more , I'm still confused...