AP Calculus AB Flashcards: Riemann Sums, Summation Notation, and Definite Integral Notation
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: July 2026
Review key ideas with interactive flashcards. This set includes 8 cards to help you master important concepts.
What two components are required to construct a Riemann sum?
A Riemann sum requires a partition of an interval into subintervals and the value of the function at a point within each of those subintervals.
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What two components are required to construct a Riemann sum?
A Riemann sum requires a partition of an interval into subintervals and the value of the function at a point within each of those subintervals.
How is a definite integral defined in relation to Riemann sums?
The definite integral of a continuous function over an interval is the limit of its Riemann sums as the widths of the subintervals approach zero.
How can a definite integral be translated back into a limit notation?
A definite integral can be translated into the limit of a related Riemann sum.
What is a Riemann sum?
A Riemann sum is the sum of products, where each product is the value of a function at a point in a subinterval multiplied by the length of that subinterval.
What does the limiting case of a Riemann sum represent?
The limiting case of a Riemann sum, as the subinterval widths approach zero, can be interpreted as and is represented by a definite integral.
What is the relationship between an approximating Riemann sum and a definite integral?
The definite integral is the precise value that the approximating Riemann sums approach as their subintervals get infinitesimally small.
How can the limit of a Riemann sum be rewritten?
The limit of a Riemann sum can be written as a definite integral.
What is the standard notation for the definite integral of a function $f$ over the interval $[a, b]$?
The definite integral is denoted by $\int_{a}^{b} f(x) dx$.