When both curves are given as y = f(x) and y = g(x), and f(x) >= g(x) on [a, b], the area between them is the integral from a to b of [f(x) - g(x)] dx. The critical first step is finding the intersection points by solving f(x) = g(x). These intersection points determine the limits of integration. Between consecutive intersection points, check which curve is on top by evaluating at any test point. If the curves switch positions, you must split the integral at every crossing point. A common error is integrating (f - g) over the entire interval without checking if g overtakes f somewhere in between.