AP®︎ Calculus BC: Topic 6.10 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 6.10 of AP Calculus BC – Integrating Functions Using Long Division and Completing the Square.

Questions List

Topic 6.10

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Question 1 Easy

A student writes ∫x2+4x+2 dx=ln⁡∣x+2∣+C\displaystyle \int \frac{x^2+4}{x+2}\,dx=\ln|x+2|+C.

Which of the following correctly explains why the student's answer is wrong?

AA quotient must be integrated by integrating its numerator and denominator separately, giving x3/3+4xx2/2+2x+C\displaystyle \frac{x^3/3+4x}{x^2/2+2x}+C.
BThe numerator is not a constant multiple of the denominator's derivative; division gives x22−2x+8ln⁡∣x+2∣+C\displaystyle \frac{x^2}{2}-2x+8\ln|x+2|+C.
CThe numerator must remain as a factor when integrating the reciprocal of the denominator, giving (x2+4)ln⁡∣x+2∣+C\displaystyle (x^2+4)\ln|x+2|+C.
DThe sum of squares in the numerator requires the inverse tangent rule rather than the logarithm rule, giving 12arctan⁡(x2)+C\displaystyle \frac{1}{2}\arctan\left(\frac{x}{2}\right)+C.

What You’re Being Tested On:

Explore the learning objectives taken directly from the College Board’s AP® Calculus BC Curriculum. Ensure you’re prepared for the exact topics covered on the AP® exam, in-class tests, and quizzes, and gain confidence in your mastery of the material.

Topic 6.10: Integrating Functions Using Long Division and Completing the Square

Learning Objective: FUN-6.D

For integrands requiring substitution or rearrangements into equivalent forms: (a) Determine indefinite integrals. (b) Evaluate definite integrals.

Essential Knowledge: FUN-6.D.3

Techniques for finding antiderivatives include rearrangements into equivalent forms, such as long division and completing the square.

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