AP®︎ Calculus AB: Topic 6.4 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 6.4 of AP Calculus AB – The Fundamental Theorem of Calculus and Accumulation Functions.

Questions List

Topic 6.4

Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
Q10
Q11
Q12
Q13
Q14
Q15

Question 1 Easy

If g(x)=∫3x1+t4 dtg(x)=\int_3^x \sqrt{1+t^4}\,dt, then g′(x)=g'(x)=

A1+x4\sqrt{1+x^4}
B2x31+x4\dfrac{2x^3}{\sqrt{1+x^4}}
C1+t4\sqrt{1+t^4}
D1+x4−82\sqrt{1+x^4}-\sqrt{82}

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 6.4: The Fundamental Theorem of Calculus and Accumulation Functions

Learning Objective: FUN-5.A

Represent accumulation functions using definite integrals.

Essential Knowledge: FUN-5.A.1

The definite integral can be used to define new functions. Illustrative example: f(x) = ∫_0^x e^t dt = e^x - 1.

Essential Knowledge: FUN-5.A.2

If f is a continuous function on an interval containing a, then d/dx ∫_a^x f(t) dt = f(x), where x is in the interval.

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