The following applet approximates the area between the curves y=f(x) and y=g(x) for a ≤ x ≤ b using Riemann Sums. Simply enter the functions f(x) and g(x) and the values a, b and 0 ≤ n ≤ 10,000, the number of subintervals. The height of each rectangle is computed using the midpoint rule and taken to be |f(x) - g(x)|. In other words, it does not matter which function is the larger of the two.

The values a and b can be changed by simply typing a new value, such as "1.2345", "pi/2", "sqrt(5)+cos(3)", etc. You may also change these values by using the up/down arrow keys or dragging the corresponding point left or right. To move the center of the graph, simply drag any point to a new location. To label the x-axis in radians (i.e. multiples of pi), click on the graph and press "control-r". To switch back, simply press "control-r" again.

Here is a list of functions that can be used with this applet.