Maple 9 Learning Guide - Maplesoft

7.1 Introductory Calculus • 233An Approximation of the Integral off(x) = 1/2+sin(x)on the Interval [0, 10]Using a Left-endpoint Riemann SumApproximate Value: 6.8390715291.510.52 4 6 8 10x–0.5–1Area: 6.845601763f(x)Change output = plot to output = sum to calculate the area of theboxes.> ApproximateInt( f(x), x=0..10, method=left, partition=6,> output=sum);( 5∑)5( 1 3 2 + sin(5 3 i)) i=0Approximately, this number is> evalf( % );6.845601766The approximation of the area improves as you increase the numberof boxes. Increase the number of boxes to 12 and calculate the value ofApproximateInt for each of these boxes.> seq( evalf(ApproximateInt( f(x), x=0..10, method=left,> partition=n^2)), n=3..14);6.948089404, 6.948819108, 6.923289158, 6.902789477,6.888196449, 6.877830055, 6.870316621, 6.864739771,6.860504866, 6.857222009, 6.854630209, 6.852550664Use the option output = animation to create an animation for theleft Riemann sum.