Riemann Sums Java Applet
Update: This applet has been updated to a mobile version. Go to: Riemann Sums.
Before integration was developed, the only way to find the area under a curve was to draw rectangles with increasingly smaller widths to get a good approximation.
Remember, we are using the area under a graph to represent some physical quantity.
For example, integration can help us to find a velocity from an acceleration, or to solve problems in electronics.
Things to Do
When you get to the new applet, you start with a predefined function that has been drawn for you. You can:
- At the bottom, increase the number of intervals (try 20). Click "Compute" and you get more rectangles and the accuracy of the approximation improves.
- Try different options from the "Method" pull-down menu. Consider which one gives the best approximation and why. You can see Trapezoid Rule in the last option.
- Change the range of values of x and y.
- Choose different example functions from the pull-down menu at the top. (Choose the example and then click "Load Example" to the left.)