Middle Boxes
The Riemann sum determined by the
midpoints is given by
which is the sum of the areas of rectangles whose heights are determined by
midpoints of subintervals.
To make a middle-boxes plot
- 1.
- Leave the insertion point inside the expression x sin x.
- 2.
- From the Calculus submenu, choose Plot Approx.
Integral.
- A middle-boxes plot appears with default range settings.
- 3.
- Click the plot to select the frame, or double-click the plot to
select the view.
- 4.
- Click the properties tool itbpF0.3009in0.3009in0.0701inproperty.wmf.
- 5.
- Reset the interval and number of boxes as desired.
- 6.
- Choose OK.
Calculus + Plot Approx. Integral
x sin x
dtbpF3in2.0003in0pt
Applied to the expression x sin x, with four rectangles and limits 0 and
3, the approximating Riemann sum is
Direct evaluation using Evaluate Numerically produces
x sin
xdx = 3.111097498