Integrals
Definition
Integrals are mathematical tools used to find the area under a curve or to calculate the accumulation of quantities over a given interval.
Analogy
Think of integrals as a way to measure how much water is in a swimming pool. Just like you can find the total amount of water by measuring the area and depth, integrals help us find the total accumulation of something by measuring its rate of change over time.
Related terms
Derivatives: Derivatives are the opposite of integrals. They measure the rate at which something changes at any given point.
Definite Integral: A definite integral calculates the exact value of an integral within specific limits or boundaries.
Indefinite Integral: An indefinite integral represents a family of functions that differ only by a constant. It helps us find antiderivatives and provides general solutions to problems involving integration.
"Integrals" appears in:
Study guides (4)
AP Calculus AB/BC - 1.7 Selecting Procedures for Determining Limits
AP Calculus AB/BC - 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals
AP Calculus AB/BC - 9.3 Finding Arc Lengths of Curves Given by Parametric Equations
AP Calculus AB/BC - 9.5 Integrating Vector-Valued Functions
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