AP Calculus AB Flashcards: Integrating Using Substitution
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.
When using substitution for a definite integral, what crucial step is required for the limits of integration?
For a definite integral, the substitution of variables requires making corresponding changes to the limits of integration.
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When using substitution for a definite integral, what crucial step is required for the limits of integration?
For a definite integral, the substitution of variables requires making corresponding changes to the limits of integration.
If an integrand is not immediately ready for substitution, what other technique might be required first?
The integrand may first require rearrangement into an equivalent form before the substitution technique can be applied.
What is an indefinite integral?
An indefinite integral is the general antiderivative of a function, representing a family of functions.
What is the substitution of variables technique?
Substitution of variables is a technique used for finding antiderivatives (indefinite integrals).
A student correctly uses substitution on a definite integral but forgets to change the limits. What will be the result?
The student will calculate an incorrect value because the original limits of integration do not correspond to the new variable.
For which type of integral—definite or indefinite—is changing the limits of integration a necessary step during substitution?
Changing the limits of integration is a necessary step specifically for evaluating definite integrals using substitution.
Why must the limits of integration be changed when evaluating a definite integral with substitution?
The original limits correspond to the original variable, so they must be changed to new values that correspond to the new substituted variable.
What two types of integral problems can be solved using substitution?
The substitution method can be used to determine indefinite integrals and to evaluate definite integrals.
What does it mean to "evaluate a definite integral"?
To evaluate a definite integral means to find the specific numerical value of the integral between its lower and upper limits.
What is the primary goal of using substitution when finding an antiderivative?
The primary goal is to transform a complicated integrand into a simpler, more basic form that can be integrated using standard rules.