MonotoneOn.intervalIntegral_deriv_mem_uIcc

∀ {f : ℝ → ℝ} {a b : ℝ}, MonotoneOn f (Set.uIcc a b) → ∫ (x : ℝ) in a..b, deriv f x ∈ Set.uIcc 0 (f b - f a)

If f is monotone on a..b, then f' is interval integrable on a..b and the integral of f' on a..b is in between 0 and f b - f a.

Defined in: Mathlib.MeasureTheory.Integral.IntervalIntegral.DerivIntegrable
Cited by: 0 results in Mathlib
Foundations: Depth 266 from the axioms · uses propext, Classical.choice, Quot.sound

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