You'll need GeoGebra for these files. It's free and awesome. Why don't you already have it? Get it here.
Evaluating a Definite Integral from a Graph
- This shows a graph composed of line segments. You can change the values of a and b to see what happens to the definite integral. Play around with it until you totally understand how these things work!
- The file does the work of drawing the rectangles. You select a, b, and the number of rectangles. It also tells you what the evaluation point is and what summation you'd enter on your calculator. Play around with it to practice writing summations.
- The graph of f(x) is shown, along with one point on the graph of g(x). The function g(x) is an accumulation of f(x). The point on g(x) can be dragged around by the user, as well as the "vertices" of f(x). When it gets too messy, hit Reset.
- You can change a and b and see what happens to the definite integral of f'(x) and on the function f(x).
- Creating a slope field on GeoGebra turned out to be...complicated. See the notes on slope fields for what each thing is doing, or just play around with it. I bet at some point slope fields will just be built in and this will have been...just a learning experience for me...