Theorems · Theorem · real analysis
integral_zpow
∀ {a b : ℝ} {n : ℤ},
0 ≤ n ∨ n ≠ -1 ∧ 0 ∉ Set.uIcc a b → ∫ (x : ℝ) in a..b, x ^ n = (b ^ (n + 1) - a ^ (n + 1)) / (↑n + 1)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 270 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- intervalIntegralstatement and proof · cited by 546
- Set.uIccstatement and proof · cited by 393
- Int.cast_oneproof · cited by 371
- Real.rpow_intCastproof · cited by 35
- integral_rpowproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- integral_powproof · cited by 8