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[Solution] The integration of a function f(x) over an interval [a, b] by the mid-point method gives an error Em, with |E_m| ≤qslant (K)/(24) ((b-a)^3)/(n^2),

Question: The integration of a function \(f(x)\) over an interval [a, b] by the mid-point

method gives an error Em, with

\[\left|E_{m}\right| \leqslant \frac{K}{24} \frac{(b-a)^{3}}{n^{2}},\]

Where \(K\) is an upper bound for \(\left|f^{\prime \prime}(x)\right|\) on [a, b] with this information, estimate

the number of partitions \(n\) needed to guarantee that the mid-point method gives a

value of \(\int_{0}^{1} e^{x^{2}} d x\)

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