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Question Number 212935 by MrGaster last updated on 27/Oct/24

$$$$$$Proving:$$$$\mid {\int }_0^{1}f\left(x\right)dx-\frac{f\left(0\right)+f\left(1\right)}{2}\mid ⩽\frac{1}{32}$$$$$$

Answered by mehdee7396 last updated on 27/Oct/24

$$forexamplef\left(x\right)=x^2\Rightarrow {\int }_0^{1}f\left(x\right)dx=\frac{1}{3}$$$$\Rightarrow \mid {\int }_0^{1}f\left(x\right)dx-\frac{f\left(0\right)+f\left(1\right)}{2}\mid =\frac{1}{6}⪇\frac{1}{32}?$$

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