Mathematics

Mathematics

Problem

Let ff be continuous, decreasing, and concave up on [2,8][2,8]. Using the same number nn of equal-width subintervals, let L, R, M,L,\,R,\,M, and TT denote the left-endpoint, right-endpoint, midpoint, and trapezoidal approximations, respectively, of ∫28f(x) dx\displaystyle \int_{2}^{8} f(x)\,dx. Which ordering from least to greatest must always hold? a) L<T<M<RL < T < M < R b) R<M<T<LR < M < T < L c) M<R<T<LM < R < T < L d) R<T<M<LR < T < M < L

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