AP®︎ Calculus BC: Topic 6.7 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 6.7 of AP Calculus BC – The Fundamental Theorem of Calculus and Definite Integrals.

Questions List

Topic 6.7

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Question 1 Easy

If GG is an antiderivative of the function ff, which of the following must be true?

AG′(x)=f(x)G'(x)=f(x) for all xx in the domain.
Bf′(x)=G(x)f'(x)=G(x) for all xx in the domain.
CG(x)=f(x)+CG(x)=f(x)+C for some constant CC.
DG′(x)=f′(x)G'(x)=f'(x) for all xx in the domain.

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 6.7: The Fundamental Theorem of Calculus and Definite Integrals

Learning Objective: FUN-6.B

Evaluate definite integrals analytically using the Fundamental Theorem of Calculus.

Essential Knowledge: FUN-6.B.1

An antiderivative of a function f is a function g whose derivative is f.

Essential Knowledge: FUN-6.B.2

If a function f is continuous on an interval containing a, the function defined by F(x) = ∫_a^x f(t) dt is an antiderivative of f for x in the interval.

Essential Knowledge: FUN-6.B.3

If f is continuous on the interval [a, b] and F is an antiderivative of f, then ∫_a^b f(x) dx = F(b) − F(a).

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