Theorems · Theorem · real analysis

intervalIntegral.integral_deriv_comp_mul_deriv

∀ {a b : ℝ} {f f' g g' : ℝ → ℝ},
  (∀ x ∈ Set.uIcc a b, HasDerivAt f (f' x) x) →
    (∀ x ∈ Set.uIcc a b, HasDerivAt g (g' (f x)) (f x)) →
      ContinuousOn f' (Set.uIcc a b) → Continuous g' → ∫ (x : ℝ) in a..b, (g' ∘ f) x * f' x = (g ∘ f) b - (g ∘ f) a

Defined in

Mathlib.MeasureTheory.Integral.IntervalIntegral.IntegrationByParts

Cited by

0 results in Mathlib

Foundations

Depth 269 from the axioms · uses propext, Classical.choice, Quot.sound