AP Calculus BC Flashcards: Approximating Areas with Riemann Sums
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 11 cards to help you master important concepts.
How can you determine if a Riemann sum approximation is an underestimate or overestimate?
Depending on the behavior of the function (e.g., increasing or decreasing), it may be possible to determine whether the approximation is an underestimate or overestimate for the definite integral.
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How can you determine if a Riemann sum approximation is an underestimate or overestimate?
Depending on the behavior of the function (e.g., increasing or decreasing), it may be possible to determine whether the approximation is an underestimate or overestimate for the definite integral.
What is the primary purpose of using Riemann sums and trapezoidal sums?
These are geometric and numerical methods used to approximate the value of a definite integral when an exact calculation is difficult or impossible.
What is the difference between uniform and nonuniform partitions in a Riemann sum?
Uniform partitions divide the interval into subintervals of equal width, while nonuniform partitions use subintervals of varying widths.
For a strictly increasing function, is a left Riemann sum an underestimate or overestimate?
For an increasing function, a left Riemann sum will be an underestimate for the value of the definite integral.
What is a right Riemann sum?
A method for approximating a definite integral by using rectangles whose height is determined by the function's value at the right endpoint of each subinterval.
List the four numerical methods for approximating definite integrals mentioned in the content.
The four methods are a left Riemann sum, a right Riemann sum, a midpoint Riemann sum, and a trapezoidal sum.
For a strictly increasing function, is a right Riemann sum an underestimate or overestimate?
For an increasing function, a right Riemann sum will be an overestimate for the value of the definite integral.
From what four types of representations can a definite integral be approximated?
Definite integrals can be approximated for functions represented graphically, numerically (table of values), analytically (an equation), and verbally.
What is a midpoint Riemann sum?
A method for approximating a definite integral by using rectangles whose height is determined by the function's value at the midpoint of each subinterval.
What is a left Riemann sum?
A method for approximating a definite integral by using rectangles whose height is determined by the function's value at the left endpoint of each subinterval.
What is a trapezoidal sum?
A method for approximating a definite integral by summing the areas of trapezoids formed by connecting the function's values at the endpoints of each subinterval.