AP Calculus BC · Unit 6: Integration and Accumulation of Change
6.9 Integrating Using Substitution
In short
This topic introduces u-substitution as a strategic technique for finding antiderivatives, specifically when the integrand is a factor of the derivative of a composite function (reversing the chain rule). You are expected to handle both indefinite and definite integrals. A critical requirement for definite integrals is that you must make corresponding changes to the limits of integration when substituting variables.
Last updated
What else do you need to know about Integrating Using Substitution?
The course emphasizes recognizing underlying patterns in integrands to choose this strategy appropriately.
How is Integrating Using Substitution tested on the exam?
Many students struggle with the relationship between differentiation and integration, mistakenly thinking integration is simply differentiation in reverse order. On the AP Exam, you must be careful when applying the chain rule during u-substitution. In free-response questions evaluated without a calculator, you must present an appropriate antiderivative and include a constant of integration for indefinite integrals. When evaluating definite integrals, you must show the expression with endpoints and an appropriately placed differential. Examiners penalize poor parentheses usage and writing strings of equal signs equating expressions that are not mathematically equal (e.g., dropping the limits of integration during the substitution steps).
Free practice questions with full explanations, and instant marking of your free-response answers.
Integrating Using Substitution: common questions
What do you need to know about Integrating Using Substitution for AP Calculus BC?
This topic introduces u-substitution as a strategic technique for finding antiderivatives, specifically when the integrand is a factor of the derivative of a composite function (reversing the chain rule). You are expected to handle both indefinite and definite integrals. A critical requirement for definite integrals is that you must make corresponding changes to the limits of integration when substituting variables.
How is Integrating Using Substitution tested on the AP Calculus BC exam?
Many students struggle with the relationship between differentiation and integration, mistakenly thinking integration is simply differentiation in reverse order. On the AP Exam, you must be careful when applying the chain rule during u-substitution.
Where does Integrating Using Substitution fit in AP Calculus BC?
Integrating Using Substitution is topic 6.9 in Unit 6: Integration and Accumulation of Change of AP Calculus BC.
Want help mastering this topic?
Work through Integrating Using Substitution one-on-one with an AP Guru tutor.
Book a free demo class