Let [a, b] be a bounded closed interval, f ∈ R[a, b] and M > 0. Suppose that |f (x)| ≤ Mfor all x ∈ [a, b]. Prove thatZ baf ≤ M (b − a)
Question
Solution 1
The statement you're asking to prove is that the integral of a function f over a closed interval [a, b] is less than or equal to M times the length of the interval, given that the absolute value of f(x) is less than or equal to M for all x in [a, b]. Here's a step-by-step proof:
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