This interactive figure illustrates numerical integration. You can change the [color=#0000ff]function using the top blue slider, or enter your own[/color]. Be sure to use only functions that are continuous on [0,4] (the interval the figure defaults back to whenever the function is changed). 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 Sum requires an even number of subintervals, so [i][math]n[/math][/i] remains even although that is not required for the Trapezoidal Sum. 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]