AP®︎ Calculus BC: 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 BC – 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
Q16
Q17
Q18
Q19

Question 1 Easy

ddx∫3x(t2+1)5 dt=\dfrac{d}{dx}\displaystyle\int_3^x (t^2+1)^5\,dt=

A(x2+1)5−105(x^2+1)^5-10^5
B10x(x2+1)410x(x^2+1)^4
C(x2+1)5(x^2+1)^5
D(t2+1)5(t^2+1)^5

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 6.4: 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 examples: f(x) = \int_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 \int_a^x f(t) dt = f(x), where x is in the interval.