2. 考研
  3. 设f’(x)在[0,1]上连续，且f(1)－f(0)=1,证明：∫01f’2(x)dx≥1.

设f’(x)在[0,1]上连续，且f(1)－f(0)=1,证明：∫01f’2(x)dx≥1.

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问题 设f’(x)在[0,1]上连续，且f(1)－f(0)=1,证明：∫01f’2(x)dx≥1.
选项
答案由1=f(1)－f(0)=∫01f’(x)dx 得12=1=(∫01f’(x)dx)2≤∫01l2dx∫01f’2(x)dx=∫01f’2(x)dx,即∫01f’2(x)dx≥1.
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考研数学二

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