Suppose we wish to find the area of a region that is bounded above by the curve [math]y=f\left(x\right)[/math], below by the curve [math]y=g\left(x\right)[/math], and on the left and right by the lines [math]x=a[/math] and [math]x=b[/math]. The area can be approximated with a Riemann sum of rectangles, where the [math]k[/math]-th rectangle has height [math]f\left(c_k\right)-g\left(c_k\right)[/math], where [math]c_k[/math] is the [math]k[/math]-th sample point in a partition of [math]\left[a,b\right][/math]. Upon taking a limit of the Riemann sums (as the norm of the partition goes to zero), we obtain the value[br] [math]\int_a^b\left[f\left(x\right)-g\left(x\right)\right]dx[/math].[br]In fact, this is how we [i]define [/i]the area of the region between the curves, whenever [math]f\left(x\right)\ge g\left(x\right)[/math] throughout [math]\left[a,b\right][/math].[br][br]In the interactive figure, several examples come preloaded. You can modify the examples, and you can pan and zoom the graphics area to suit your needs.