The definite integral computes the signed area between and the -axis. When you want the area between two curves — a demand curve and a supply curve, an option payoff and a straight-line hedge — the integrand becomes the vertical gap . This lesson builds the basic area-between-curves formula (vertical integration), explains what happens when the curves cross, and introduces horizontal integration for functions of . The consumer-and-producer-surplus formulas in economics are a direct application.
Learning objectives. By the end of this note you should be able to:
- write down the area formula for a region bounded above by and below by ;
- find intersection points and split the integral when curves cross;
- set up an area integral integrating with respect to when that is more efficient;
- compute consumer and producer surplus from demand and supply functions.
In this lesson
- Area between two curves (vertical strips)
- When curves cross: splitting the integral
- Area by horizontal integration
- Finance application: consumer and producer surplus
Before you start
- The Fundamental Theorem of Calculus
- Indefinite Integrals, the Net Change Theorem, and the Substitution Rule
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