How do I find the area enclosed between two curves, like a parabola and a line?
First find where they meet by setting the two functions equal — these intersection points are your limits a and b.
First find where they meet by setting the two functions equal — these intersection points are your limits a and b. Decide which curve is on top over that interval, then integrate the difference: Area = ∫ₐᵇ (upper − lower) dx. Subtracting the lower curve from the upper automatically handles the region between them, and using the intersection points as limits ensures you capture exactly the enclosed area.
Key point
Area between curves = ∫ (upper − lower) dx, with limits at their intersection points.
Common mistake
forgetting to find the intersection points that set the limits.
Memory tip
intersections give the limits; integrate top minus bottom.
Tap to watch or see it right here — the app stays open (it only opens a quick search if nothing embeddable is found).