Riemann sums
How can we estimate the area under a curve?
If I want to find the area between the graph of a function y=f(x) and between some points a and b on the x-axis, how can I do that?
One strategy is to estimate by drawing rectangles that are similar to the area I'm trying to estimate.
Activity
1. Click on the box that says "Show Rectangles". You should see one large rectangle. Is the rectangle the same as the area you are trying to find? Is it close?
2. Use the slider to increase the number of rectangles, or n.
3. Check the box to see the area of all your rectangles added together.
Questions to think about
What happens to our estimate as n increases?