The applet illustrates the geometric interpretation of antiderivatives in terms of areas. It also illuminates the concept of accumulated change: the total change is the definite integral of the rate of change.
Click the screen shot below to open the applet in a new window:
The user can enter a formula and the applet will graph an arbitrary function. The user can try to sketch the antiderivative of the function (with a given initial condition) by drawing on screen with the mouse. The actual graph of the antiderivative is revealed point by point as the user drags a slider. At the same time, the area corresponding to the value of the antiderivative is dynamically shaded. Many demo examples are provided. The applet will display antiderivatives of functions hand-drawn by the user as well as those defined by formulas.