- #1

peripatein

- 880

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## Homework Statement

I was asked to prove that for f(x), Riemann integrable and bounded from above by real number M:

∫[a,b] f(x) < M(b-a)

## Homework Equations

## The Attempt at a Solution

Since f(x) is Riemann integrable, ∫[a,b] f(x) must be equal to both the lower and upper Darboux sums. Therefore: ∫[a,b] f(x) = supf(x)

_{[a,b]}Ʃ[i=1,n]Δx

_{i}= supf(x)

_{[a,b]}(b-a) <= M(b-a)

I am really not sure this is rigorous enough, or even how it ought to be approached. I'd appreciate some guidance please.