Lower und Upper Sum of a Function
Here, you can see a function with its lower sum and upper sum on the interval [a, b].

Drag the endpoints a and b of the interval with the mouse. What
characteristics of the rectangles of the (a) lower sum, (b) upper sum do you
see? Write down your observations.

Now, change the number of rectangles n by moving the slider with
the mouse. How does this affect the difference between lower and upper sum?
Write down your conjectures.

Do your conjectures of (2) hold for other intervals [a,
b]? Check this by changing both the interval end points and the number of
rectangles.
Created with GeoGebra
by Markus Hohenwarter
