AP Calculus BC · Unit 6: Integration and Accumulation of Change
6.13 Evaluating Improper Integrals
In short
This topic introduces improper integrals, which are strictly part of the BC curriculum. The scope includes integrals where one or both limits of integration are infinite, as well as integrals where the integrand has an infinite discontinuity (is unbounded) anywhere within the interval of integration.
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What else do you need to know about Evaluating Improper Integrals?
You are required to formally evaluate these by setting up and calculating the limits of definite integrals, or to conclude that the integral diverges if the limit does not exist.
Can you do these?
- I can identify an improper integral by checking if it has infinite limits or an unbounded integrand.
- I can evaluate improper integrals by setting up and calculating the limits of definite integrals.
How is Evaluating Improper Integrals tested on the exam?
This topic is paired with the skill 'Implementing Mathematical Processes' (1.E). On the AP Exam, particularly in Free-Response Questions (FRQs), examiners expect to see the formal limit notation explicitly written out when transitioning from the improper integral to the definite integral. A common pitfall is evaluating the integral using infinity as a standard bound without writing the limit, which typically results in a penalty or loss of the communication/setup mark.
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Evaluating Improper Integrals: common questions
What do you need to know about Evaluating Improper Integrals for AP Calculus BC?
This topic introduces improper integrals, which are strictly part of the BC curriculum. The scope includes integrals where one or both limits of integration are infinite, as well as integrals where the integrand has an infinite discontinuity (is unbounded) anywhere within the interval of integration.
How is Evaluating Improper Integrals tested on the AP Calculus BC exam?
This topic is paired with the skill 'Implementing Mathematical Processes' (1.E). On the AP Exam, particularly in Free-Response Questions (FRQs), examiners expect to see the formal limit notation explicitly written out when transitioning from the improper integral to the definite integral.
How do I know I have mastered Evaluating Improper Integrals?
Check you can do each of these: identify an improper integral by checking if it has infinite limits or an unbounded integrand; evaluate improper integrals by setting up and calculating the limits of definite integrals.
Where does Evaluating Improper Integrals fit in AP Calculus BC?
Evaluating Improper Integrals is topic 6.13 in Unit 6: Integration and Accumulation of Change of AP Calculus BC.
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