Definite Integral Approximations

Topic:Area, Calculus, Definite Integral, Integral Calculus, Trapezoid, Upper and Lower Sum or Riemann Sum

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 f(x) 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 to set the number of subintervals/rectangles. Observe the effect of increasing the number of subintervals and compare the different methods. 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.

Definite Integral Approximations

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