AP®︎ Calculus AB: Topic 6.9 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 6.9 of AP Calculus AB – Integrating Using Substitution.

Questions List

Topic 6.9

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Question 1 Easy

Let FF and gg be differentiable functions with F′(x)=f(x)F'(x)=f(x). Which expression gives ∫f(g(x)) g′(x) dx\int f(g(x))\,g'(x)\,dx in general?

AF(g(x))+CF(g(x))+C
BF(g(x)) g(x)+CF(g(x))\,g(x)+C
CF(g(x)) g′(x)+CF(g(x))\,g'(x)+C
Df(g(x))+Cf(g(x))+C

What You’re Being Tested On:

Explore the learning objectives taken directly from the College Board’s AP® Calculus AB 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 6.9: Integrating Using Substitution

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.1

Substitution of variables is a technique for finding antiderivatives.

Essential Knowledge: FUN-6.D.2

For a definite integral, substitution of variables requires corresponding changes to the limits of integration.

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