设f(x)在[0,1]上有连续导数,且f(0)=f(1)=0,证明|∫(0,1)f(x)dx|≤1/4max(0≤x≤1)|f'(x)|
问题描述:
设f(x)在[0,1]上有连续导数,且f(0)=f(1)=0,证明|∫(0,1)f(x)dx|≤1/4max(0≤x≤1)|f'(x)|
答
设f(x)在[0,1]上有连续导数,且f(0)=f(1)=0,证明|∫(0,1)f(x)dx|≤1/4max(0≤x≤1)|f'(x)|