Integration
Definition
Integration is an operation in calculus that finds antiderivatives, or reverse derivatives, allowing us to calculate areas, volumes, and other quantities related to curves and functions.
Analogy
Think of integration as putting puzzle pieces together. Each small piece represents an infinitesimally small change in quantity, and integrating them all adds up to give you the complete picture or total value.
Related terms
Indefinite Integral: An integral without specified limits that gives a family of functions as its result.
Fundamental Theorem of Calculus: This theorem establishes a connection between differentiation and integration, stating that differentiation undoes what integration does.
Integration by Parts: A technique used to evaluate integrals involving products of functions by applying a specific formula derived from the product rule for differentiation.
"Integration" appears in:
Subjects (6)
Study guides (5)
AP Calculus AB/BC - 6.12 Integrating Using Linear Partial Fractions
AP Calculus AB/BC - 8.8 Volumes with Cross Sections: Triangles and Semicircles
AP Calculus AB/BC - 8.9 Volume with Disc Method: Revolving Around the x- or y-Axis
AP Calculus AB/BC - 8.11 Volume with Washer Method: Revolving Around the x- or y-Axis
AP Calculus AB/BC - 9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve
Additional resources (2)
Practice Questions (2)
- What is the definition of integration in calculus?
- Which step allows integration to be performed on both sides of the equation in the process of finding a particular solution?
Resources
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