Area Under Curve Calculator
f(x) = c₂x² + c₁x + c₀, area between x = a and x = b
How This Is Calculated
The area under a curve from a to b is the definite integral ∫[a,b] f(x)dx, evaluated as F(b) − F(a) where F is the antiderivative — the Fundamental Theorem of Calculus in action. When the curve dips below the x-axis, the signed result goes negative even though physical area is always positive. Full reasoning in the Integration Shortcuts guide, or find any polynomial's integral directly with the Polynomial Integral Calculator.