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. Alternately, 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: Shift and click-drag to pan left/right/up/down. Shift and click-scroll to zoom in and out. 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.