Theorems · Theorem · real analysis
integral_rpow
∀ {a b r : ℝ}, -1 < r ∨ r ≠ -1 ∧ 0 ∉ Set.uIcc a b → ∫ (x : ℝ) in a..b, x ^ r = (b ^ (r + 1) - a ^ (r + 1)) / (r + 1)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 269 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Complexproof · cited by 5,565
- MeasureTheory.integralproof · cited by 1,779
- Complex.ofRealproof · cited by 1,654
- MeasureTheory.Measure.restrictproof · cited by 1,646
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- Complex.reproof · cited by 882
- intervalIntegralstatement and proof · cited by 546
- Set.uIccstatement and proof · cited by 393
- RCLike.reproof · cited by 319
Cited by4
Results whose statement or proof uses this declaration.
- ZetaAsymptotics.term_oneproof · cited by 1
- MeasureTheory.lintegral_rpow_eq_lintegral_meas_le_mulproof · cited by 1
- integral_zpowproof · cited by 1
- ZetaAsymptotics.term_of_ltproof · cited by 1