Tutorial:Creating and Enhancing Dynamic Worksheets with GeoGebra

Lower and Upper Sum

You will now learn how to create a dynamic worksheet that illustrates how lower and upper sums can be used to approximate the area between a function and the x-axis, which can be used to introduce the concept of integral to students.

Preparations

• Open a new GeoGebra window.
• Switch to Perspectives – Algebra & Graphics.

Construction Steps

1		Enter the cubic polynomial f(x) = -0.5x3 + 2x2 – x + 1.
2		Create two points A and B on the x-axis. Hint: These points will determine the interval which restricts the area between the function and the x-axis.
3		Create slider for the number n with Interval 1 to 50 and Increment 1.
4		Enter uppersum = UpperSum[f, x(A), x(B), n]. Hint: x(A) gives you the x-coordinate of point A. Number n determines the number of rectangles used in order to calculate the lower and upper sum.
5		Enter lowersum = LowerSum[f, x(A), x(B), n].
6		Insert dynamic text Upper Sum = and select uppersum from Objects.
7		Insert dynamic text Lower Sum = and select lowersum from Objects.
8		Calculate the difference diff = uppersum – lowersum.
9		Insert dynamic text Difference = and select diff from Objects.
10		Enter integral = Integral[f, x(A), x(B)].
11		Insert dynamic text Integral = and select integral from Objects.
12		Fix slider and text using the Properties Dialog.