The area problem asks how we can determine the area under a non-straight curve. It turns out that we can approximate the area using rectangles. The more rectangles we use, the better our approximation to the area is.
The applet below allows you to use different numbers of rectangles to approximate the area. The exact area (to ten significant digits) is given first, followed by the approximate area using rectangles. The difference between the exact answer and the approximate answer is given as the percent error of the approximation.
In Chapter 4 we'll discuss how to find the area exactly by considering what would happen if we could use an infinitely large number of infinitely thin rectangles.