Definite integral
This original textbook reading covers part of the AP topic. Follow the AP course outline for complete topic instruction and practice.
- Definite integral
The definite integral of a function has upper and lower bounds signifying the interval over which its area is to be calculated. Its solution is simply the anti-derivative evaluated at the upper bound minus its anti-derivative evaluated at the lower bound, as shown by the second fundamental theorem of calculus
- Related Glossary Terms
Anti-derivative, Anti-Power Rule, Indefinite integral, Integral rules, Second Fundamental Theorem of Calculus, Trigonometric substitution, U-substitution
- Index
Chapter 8 - Notation and Rules
Chapter 8 - FFR - Substitution and Differentials
Chapter 8 - FFR - Substitution and Differentials
Glossary and deeper reading · 1 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
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Definite integral
A definite integral accumulates a function over a specified interval as a limit of Riemann sums when that limit exists. Its sign includes the function’s sign and the orientation of the limits. For example, the integral of the constant −2 from 0 to 3 is −6, although the geometric area is 6. In a rate model, the result has rate units multiplied by input units.