Enrich · Mathematics Advanced 11–12 – Year 12 · Integral calculus
Enrich Use a graphing application to compare different methods of approximating the area, A, of the region between the continuous function y = f(x) and the x -axis, where f(x) ≥ 0 on the interval a ≤ x ≤ b, by summing the areas of trapezia or rectangles each of width Δx = (b - a)/n and approximate height f(x) for any x lying in its base, and observe the effect on the precision of the approximation of A as the number n of subintervals of a ≤ x ≤ b increases, that is as Δx→0
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