f(x)＝lnsinx是初等函數(shù),在[π/6,5π/6]上有定義,所以f(x)在[π/6,5π/6]上連續(xù).
在定義域內(nèi),f'(x)＝tanx,所以f(x)在(π/6,5π/6)內(nèi)可導(dǎo).
f(5π/6)＝f(π/6)＝ln(1/2).
由羅爾定理,至少存在一點(diǎn)ξ∈(π/6,5π/6),使得f'(ξ)＝0.而f'(π/2)＝0,π/2∈(π/6,5π/6).
所以羅爾定理對(duì)函數(shù)y=lnsinx在區(qū)間[π/6,5π/6]上正確.