The Fundamental Theorem of Calculus. Definite integral equals antiderivative evaluated at bounds.
Physics — Total distance traveled: ∫v dt from t₁ to t₂.
Engineering — Area under load-deflection curves.
Economics — Consumer/producer surplus calculations.
Statistics — Probability between two values: P(a<X<b) = ∫f(x)dx.
Medicine — Total drug exposure (AUC - Area Under Curve).
Hydrology — Total water flow over a time period.
Environmental — Total pollution released.
Manufacturing — Total production over a shift.
Finance — Present value of cash flow stream.
Physics — Work done by variable force.
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