Definite Integral Approximations

This worksheet is intended to help the student compare and contrast the various methods for approximating or calculating definite integrals: Left/Middle/Right sums, Upper sums, Lower sums, Trapezoidal sums, and the Definite Integral itself.
Either use the default function or enter a function of your choice. Alternatively, drag (translate) the existing curve to a new position on the x-y plane. It will be especially useful to know how to pan or zoom within this worksheet.
  • On a touchscreen, the usual pinching and swiping should be straight-forward.
  • With a mouse and keyboard, click and drag on any open part of the graphics region to pan left/right/up/down. (i.e. Don't click and drag on an object.) A mouse scroll will may zoom in and out, although the Zoom buttons may offer finer control. Also, to re-scale either axis, Shift and click-drag along the axis.
On the graph, drag the points A and B along the x-axis to adjust the interval. Select the checkboxes corresponding to the method(s) that you want to use for calculating/approximating the definite integral. For the "Left/Mid/Right Sum, observe how adjusting the slider affects the sub-interval regions being calculated. Adjust the "n" slider. Observe the effect of increasing the number of sub-intervals and compare the different methods.