Riemann Sums Java Applet

Update: This applet has been updated to a mobile version. Go to: Riemann Sums.

You can use this Java applet to explore the concept of numerical integration. We met this concept before in Trapezoidal Rule and Simpson Rule.

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.)