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Let-a-differentiable-function-f-R-R-satisfies-f-x-1-for-all-x-0-2-and-f-0-f-2-1-Prove-that-1-0-2-f-x-dx-3-

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Question Number 105742 by ZiYangLee last updated on 31/Jul/20
Let a differentiable function f:R→R satisfies ∣f′(x)∣≤1 for all x∈[0,2] and f(0)=f(2)=1 Prove that 1≤∫_0 ^2 f(x)dx≤3
Letadifferentiablefunctionf:R→Rsatisfies∣f′(x)∣⩽1forallx∈[0,2]andf(0)=f(2)=1Provethat1⩽∫02f(x)dx⩽3

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