Mathematics

Mathematics

Problem

Six equal-width subintervals partition [0,3][0,3]. For each subinterval, a rectangle is drawn whose height is h(x)h(x) evaluated at the point halfway through that subinterval, where h(x)=x3h(x)=x^{3}. Which of the following is the resulting estimate of ∫03h(x) dx\displaystyle \int_{0}^{3} h(x)\,dx? a) 20.8120.81 b) 19.9719.97 c) 20.2520.25 d) 19.8519.85

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