Integration
The mathematical process of finding the area under a curve or accumulation of a quantity.
Also: integral · antiderivative
Definition
Integration is a fundamental operation in calculus that can be interpreted as finding the area under a curve, the accumulation of a continuously changing quantity, or the inverse operation of differentiation (as stated in the Fundamental Theorem of Calculus). Definite integrals compute a numerical value over an interval, while indefinite integrals produce a family of functions. Integration is essential in physics, engineering, economics, and statistics.
Example
“An engineer calculates the total distance traveled by a rocket during its 10-minute burn by integrating the rocket's velocity function over time, finding the area under the velocity-time curve.”
Synonyms
- antiderivative
- integral calculus
- area under curve
Antonyms / Opposites
- differentiation
- derivative
Images
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Related Terms
- Differentiation
- Fundamental Theorem of Calculus
- Differential Equation
- Area Under Curve