Free response without a calculator (Part B)
BC: Integration techniques, improper integrals and arc length
- Units 6 and 8
- 9 points
- About 15 minutes
- BC only
A multi-part problem you solve by hand, often from a graph, a table, an equation or a differential equation. You show your work, use exact values, and justify answers with calculus reasons such as a sign change in a derivative or the conditions of a theorem. On the exam: 4 questions in Part B of the free-response section (60 minutes, no calculator). The whole free-response section is 6 questions in 90 minutes and counts for 50% of the score. AB and BC use the same format; on BC, Part B usually includes a series question and a question on BC-only topics.
The question
Answer each part without a calculator, showing the work that leads to your answer.
Suggested time: 15 minutes
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Part (a)
3 pointsEvaluate the improper integral ∫₂^∞ 6/(x² + x − 2) dx or show that it diverges. Use limit notation for the improper integral.
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Part (b)
3 pointsEvaluate ∫₀^∞ x·e^(−x/2) dx or show that it diverges. Use limit notation for the improper integral.
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Part (c)
3 pointsFind the length of the curve y = (2/3)x^(3/2) from x = 0 to x = 3.
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