Area Between Two Curves
Formula: A = ∫ from a to b |f(x) - g(x)| dx
Or equivalently: ∫(top function - bottom function)dx
Method:
1. Graph both functions (or sketch)
2. Find intersection points (set f(x) = g(x), solve)
3. Determine which function is on top in each interval
4. Integrate (top - bottom) over each interval
Horizontal slicing: Sometimes easier to integrate with respect to y.
A = ∫ from c to d (right function - left function) dy
AP exam: Area between curves appears on free response regularly. Show your setup clearly — the integral with correct limits earns points even if arithmetic is wrong.
Reference:
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