Area between curves
Calculate the area enclosed between two curves f(x) and g(x) from a to b.
f(x) =
g(x) =
From x =
to x =
Formula
A = ∫ₐᵇ |f(x) − g(x)| dx
When f(x) ≥ g(x) on [a,b]: A = ∫ₐᵇ [f(x) − g(x)] dx
Finding intersection points
If bounds aren't given, set f(x) = g(x) and solve for x to find where the curves intersect.
Example
Area between y=x² and y=x from 0 to 1: A = ∫₀¹ (x − x²) dx = [x²/2 − x³/3]₀¹ = 1/2 − 1/3 = 1/6.
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