Mathematics, 14.03.2022 15:00 reghanhoward3

Given f(x) > 0 with f ′(x) < 0, and f ′′(x) < 0 for all x in the interval [0, 1] with f(0) = 1 and f(1) = 0.3, the left, right, trapezoidal, and midpoint rule approximations were used to estimate the integral from 0 to 1 of f of x, dx. The estimates were 0.7915, 0.8405, 0.8410, 0.8421 and 0.8895, and the same number of subintervals were used in each case. Match the rule to its estimate.

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Given f(x) > 0 with f ′(x) < 0, and f ′′(x) < 0 for all x in the interval [0, 1] with f(0)...