This worksheet is intended to help the student compare and contrast the various methods for approximating or calculating definite integrals:[br]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.[br]Alternatively, drag (translate) the existing [i]f[/i]([i]x[/i]) curve to a new position on the x-y plane.[br][br]It will be especially useful to know how to pan or zoom within this worksheet.[br][list][*]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.[/*][/list][br]On the graph, drag the points [color=#741b47][b]A[/b][/color] and [b][color=#741b47]B[/color][/b] along the x-axis to adjust the interval.[br]Select the checkboxes corresponding to the method(s) that you want to use for calculating/approximating the definite integral.[br]For the "Left/Mid/Right Sum, observe how adjusting the slider affects the sub-interval regions being calculated.[br]Adjust the [b][color=#741b47]n[/color][/b] slider to set the number of subintervals/rectangles. Observe the effect of increasing the number of subintervals and compare the different methods.[br][br]Rather than dragging any points or sliders, you may achieve finer control by selecting the object and then using arrow buttons on a keyboard ← → ↑ ↓. Holding shift while pressing an arrow key will decrease the increment value, or holding control while pressing an arrow key will increase the increment value.