31. (a) Use the Midpoint Rule and the given data to estimate the value of the integral (32 f(x) dx. x 0.0 0.4 0.8 1.2 1.6 f(x) x 2.0 2.4 2.8 3.2 6.8 6.5 6.3 6.4 6.9 f(x) 7.6 8.4 8.8 9.0 (b) If it is known that −4 ≤ ƒ"(x) ≤ 1 for all x, estimate the error involved in the approximation in part (a).

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