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.”
Usage Examples
- 1
“The team applied integration best practices to improve their mathematics outcomes significantly.”
- 2
“Understanding integration is essential for anyone building a career in STEM.”
When & How to Use
Use 'Integration' when working in Mathematics contexts where 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).
- ▸Applying integration principles during a mathematics project or initiative
- ▸Explaining integration to a junior team member or stakeholder unfamiliar with STEM
- ▸Evaluating options or proposals using integration as a decision-making criterion
Etymology & Origin
The term 'Integration' derives from Latin roots and entered STEM professional usage as the field formalised in the 20th century.
History & Evolution
The concept of integration has evolved alongside STEM. Early practitioners relied on informal methods; structured approaches emerged with the professionalisation of mathematics in the mid-20th century. Today, integration is a standard part of STEM practice globally.
Synonyms
- antiderivative
- integral calculus
- area under curve
Antonyms / Opposites
- differentiation
- derivative
Images
CC-licensed · free to useVideo
Related Terms
- Differentiation
- Fundamental Theorem of Calculus
- Differential Equation
- Area Under Curve