Mathematics

Mathematics

Problem

Let f(x)=3xf(x)=3\sqrt{x}. Two equal-width subintervals partition [1,5][1,5], and the height of each rectangle is chosen to be f(2)f(2) and f(4)f(4), respectively. Which value is the best estimate of ∫15f(x) dx\displaystyle \int_{1}^{5} f(x)\,dx obtained from these two rectangles? a) 24.824.8 b) 19.219.2 c) 20.520.5 d) 22.122.1

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