AP Calculus AB Flashcards: Applying Properties of Definite Integrals
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 10 cards to help you master important concepts.
What is the property of definite integrals concerning the sum of two functions?
The integral of the sum of two functions over an interval is equal to the sum of the individual integrals of each function over that same interval.
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What is the property of definite integrals concerning the sum of two functions?
The integral of the sum of two functions over an interval is equal to the sum of the individual integrals of each function over that same interval.
How can you find the integral over a large interval if you know the integrals over two smaller, adjacent intervals that compose it?
Using the property of adjacent intervals, you can add the values of the integrals of the two smaller intervals to find the value of the integral over the entire interval.
If a function's graph has a single removable discontinuity within an interval, can you still evaluate its definite integral?
Yes, the definite integral can be evaluated because its definition can be extended to functions with removable discontinuities.
If you know the integral of f(x) from a to b, how does reversing the limits of integration (from b to a) affect the result?
The property for the reversal of limits of integration states that the integral from b to a is the negative of the integral from a to b.
What are the two main approaches mentioned for calculating a definite integral?
A definite integral can be calculated by using areas and geometry or by applying the properties of definite integrals.
Can the concept of a definite integral be applied to functions that are not continuous?
Yes, the definition of the definite integral may be extended to functions that have removable or jump discontinuities.
List four key properties of definite integrals.
Properties include the integral of a constant times a function, the integral of the sum of two functions, reversal of limits of integration, and the integral of a function over adjacent intervals.
What does the property for the integral of a constant times a function state?
The integral of a constant multiplied by a function is equal to the constant multiplied by the integral of the function.
What is a method for evaluating a definite integral that relies on its graphical representation?
A definite integral can be evaluated by using geometry and the connection between the definite integral and area, especially when the function's graph forms a simple shape.
Why is the connection between a definite integral and area a useful tool for evaluation?
This connection is useful because in some cases, the area under a curve can be calculated using simple geometric formulas, providing a direct way to find the integral's value.