This interactive figure illustrates the approximation of the area under a curve using the [color=#ff7700][b]left endpoints[/b][/color], [color=#1e84cc][b]right endpoints[/b][/color], and [color=#9900ff][b]midpoints[/b][/color], computed using [math]n[/math] rectangles.[br][br]In any of these three cases, as [math]n\to\infty[/math], note how the sum of the areas of these rectangles approach the exact value of the definite integral. This is why the definite integral is written as a [i]limit![/i]

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