StellarIf two curves intersect more than twice, then the “top minus bottom” or “right minus left” relationship may change across the interval. In that situation, you usually split the region into multiple subintervals and add the separate areas. Another valid approach is using the absolute value of the difference, but on AP problems it is often clearer to break the region at the intersection points and write more than one definite integral. The key idea is that area must always be positive, so whenever the curves switch order, your setup must account for that.
You should first find all intersection points in the interval, then determine which function is on top or on the right on each subinterval. After that, you write one integral for each piece and add them. This lesson is really an extension of 8.4 and 8.5, but it requires more attention to how the region changes across the interval. The calculus is not harder than before; the main challenge is setting up the geometry correctly.