Mathematics

Mathematics

Problem

The function hh is increasing on the interval [2,7][2,7]. A student partitions the interval at x=2,3,5,7x=2,3,5,7 and approximates ∫27h(x) dx\displaystyle \int_{2}^{7} h(x)\,dx by summing rectangles whose heights are the values of hh at the left endpoints of the subintervals. Will the student’s estimate be less than, equal to, or greater than the exact value of the integral? Briefly state the correct comparison.

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