This interactive figure illustrates numerical integration. Select an example from the dropdown list, or enter your own. Be sure to use only functions that are continuous over your interval of integration. Drag the [color=#38761d]green points[/color] on the [math]x[/math]-axis to change the limits of integration.[br][br]You can change the number of subintervals [i][math]n[/math][/i] using the slider labeled [math]n[/math]. You will not see the effect until you have selected a method. Simpson's Rule requires an even number of subintervals, so [i][math]n[/math][/i] remains even even though that is not required for the Trapezoidal Rule. You can select to show any combination of [color=#ff0000]Trapezoidal Sum[/color], [color=#38761d]Simpson's Sum[/color], or [color=#9900ff]the actual value[/color] (obtained by evaluating the integral or the approximation the computer generates in the case of a function that cannot be integrated).

[i]Developed for use with Thomas' Calculus, published by Pearson.[/i]