In addition to finding the area under a single curve, integrals can also be used to calculate the area between multiple curves. This advanced application allows us to determine the enclosed region between two or more functions.

To find the area between two curves, we need to first identify the x-values where the curves intersect. We then integrate the difference between the upper and lower curves over the interval between these intersection points. The resulting value gives us the area of the region bounded by the curves.

For example, consider the curves y = x^2 and y = x. To find the area between these two curves, we must determine the x-values where they intersect. Solving the equation x^2 = x, we find x = 0 and x = 1. We can then integrate the function (x^2 - x) from x = 0 to x = 1 to find the area between the two curves.

By applying the concepts of integration and finding areas between curves, we can tackle even more complex problems and gain a deeper understanding of the fundamental theorem of calculus.