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`BookProof.WeakSecondDeriv.integral_eq_neg_integral_coord_mul_deriv` {g : ℝ → ℝ} (h : IsTestFun g) : ∫ x, g x = -∫ x, x * deriv g x

Proved
BookProof.WeakSecondDeriv.integral_eq_neg_integral_coord_mul_deriv

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeakSecondDerivative.

BookProof.WeakSecondDeriv.integral_eq_neg_integral_coord_mul_deriv {g : ℝ → ℝ} (h : IsTestFun g) : ∫ x, g x = -∫ x, x * deriv g x

Formalization note: Lean 4 identifier BookProof.WeakSecondDeriv.integral_eq_neg_integral_coord_mul_deriv.

Preamble
-- Generated from ChapterWeakSecondDerivative.lean — theorem BookProof.WeakSecondDeriv.integral_eq_neg_integral_coord_mul_deriv
import Mathlib
import Definitions.Def_ChapterWeakSecondDerivative
open BookProof.WeakSecondDeriv



open MeasureTheory Filter Topology intervalIntegral Set

noncomputable section
Formal statement
theorem BookProof.WeakSecondDeriv.integral_eq_neg_integral_coord_mul_deriv {g : ℝ → ℝ} (h : IsTestFun g) :
    ∫ x, g x = -∫ x, x * deriv g x := by sorry

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