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AP Calculus AB 6.10 Integration by Long Division and Completing the Square Question Bank

Practise integration questions that require algebraic rearrangement, polynomial long division or completing the square before integrating.

Syllabus
Effective Fall 2025
Course
AP Calculus AB

Exam points

  • rearrange rational or quadratic expressions before integrating
  • use long division or completing the square to select a valid antiderivative

FUN-6.D—For integrands requiring substitution or rearrangements into equivalent forms: (a) Determine indefinite integrals. (b)…—Topic 6.10 question 1

[Maximum number: 1]

egral from 0 to 2 of start fraction numerator x squared end exponent minus 3 x plus 7 over denominator x plus 3 end fraction d x equals

A

Over 3

B

egative 10 plus 25 times natural log of 5 over 3

C

plus 7 times natural log of 5 over 3

D

tart fraction 32 over 5 end fraction times natural log⁡\log of 5

Table for Question FUN-6.D—For integrands requiring substitution or rearrangements into equivalent forms: (a) Determine indefinite integrals. (b)…—Topic 6.10 question 1 — AP Calculus AB
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