Definite Integrals
Definition
Definite integrals are used to find the exact value of the area under a curve between two points on the x-axis. It represents the accumulation of infinitesimally small areas and can be thought of as finding the total "signed" area.
Related terms
Antiderivatives: Antiderivatives are functions that "undo" derivatives. They represent families of functions that have the same derivative.
Riemann Sums: Riemann sums are approximations of definite integrals by dividing an interval into smaller subintervals and summing up areas using rectangles or trapezoids.
Fundamental Theorem of Calculus: The fundamental theorem of calculus establishes a connection between definite integrals and antiderivatives, stating that if F(x) is an antiderivative of f(x), then ∫[a,b] f(x) dx = F(b) - F(a).
"Definite Integrals" appears in:
Additional resources (1)
AP Calculus AB/BC - 2024 AP Calculus AB Exam Guide
Practice Questions (8)
Which property of definite integrals states that the integral of a sum of two functions is equal to the sum of their individual integrals?
What property of definite integrals states that the integral of a function over the interval [a, b] is equal to the negative of the integral of the same function over the interval [b, a]?
Which property of definite integrals states that the integral of a function over the interval [a, a] is always zero?
What property of definite integrals states that the integral of a function over the interval [a, b] is equal to the integral of the same function over the interval [c, b] plus the integral of the same function over the interval [a, c]?
Which property of definite integrals states that the integral of a function is unchanged when its limits of integration are reversed?
What property of definite integrals states that the integral of a constant function over any interval is equal to the product of the constant and the length of the interval?
What property of definite integrals states that the integral of a function over an interval is equal to the integral of the same function over a partition of that interval?
Which of the following is a common method for evaluating definite integrals?
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AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.