Theorems · Theorem · special functions
integral_log_sin_zero_pi
∫ (x : ℝ) in 0..Real.pi, Real.log (Real.sin x) = -Real.log 2 * Real.pi
The integral of log ∘ sin on 0 … π equals -log 2 * π.
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- Foundations
- Depth 274 from the axioms · uses propext, Classical.choice, Quot.sound
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- Realstatement and proof · cited by 25,697
- Real.pistatement and proof · cited by 1,774
- MeasureTheory.MeasureSpace.volumestatement · cited by 1,323
- Real.logstatement and proof · cited by 939
- intervalIntegralstatement · cited by 546
- Real.sinstatement · cited by 389
- integral_log_sin_zero_pi_div_twoproof · cited by 1
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