Maple 9 Learning Guide - Maplesoft

4.2 The Maple Packages • 93You can find the area under the curve between these two points byusing Riemann sums.> ApproximateInt(-2/3*x^2+x, x=0..3/2, method=midpoint,> output=plot, view=[0..1.6, -0.15..0.4]);0.4An Approximation of the Integral off(x) = –2/3*x^2+xon the Interval [0, 3/2]Using a Midpoint Riemann SumApproximate Value: .37500000000.30.20.10–0.10.2 0.4 0.6 0.8 1 1.2 1.4 1.6x–0.2Area: .3768750000f(x)Since the result is not a good approximation, increase the number ofboxes used to forty.> ApproximateInt(-2/3*x^2+x, x=0..3/2, method=midpoint,> output=plot, view=[0..1.6, -0.15..0.4],> partition=40);0.4An Approximation of the Integral off(x) = –2/3*x^2+xon the Interval [0, 3/2]Using a Midpoint Riemann SumApproximate Value: .37500000000.30.20.10–0.10.2 0.4 0.6 0.8 1 1.2 1.4 1.6x–0.2Area: .3751171867f(x)To determine the actual value, take the limit as n goes to ∞. Use nboxes and change the output to sum .> ApproximateInt(-2/3*x^2+x, x=0..3/2, method=midpoint,> output=sum, partition=n);