AP®︎ Calculus BC: Topic 9.5 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 9.5 of AP Calculus BC – Integrating Vector-Valued Functions.

Questions List

Topic 9.5

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Q9

Question 1 Easy

Find ∫⟨6t2−1, e3t⟩ dt\displaystyle \int \langle 6t^2-1,\ e^{3t}\rangle\,dt. In each option, C\mathbf{C} is an arbitrary constant vector.

A⟨2t3−t, 3e3t⟩+C\left\langle 2t^3-t,\ 3e^{3t}\right\rangle+\mathbf{C}
B⟨6t3−t, 13e3t⟩+C\left\langle 6t^3-t,\ \frac{1}{3}e^{3t}\right\rangle+\mathbf{C}
C⟨2t3−t, 13e3t⟩+C\left\langle 2t^3-t,\ \frac{1}{3}e^{3t}\right\rangle+\mathbf{C}
D⟨6t3−t, 3e3t⟩+C\left\langle 6t^3-t,\ 3e^{3t}\right\rangle+\mathbf{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 9.5: Integrating Vector-Valued Functions

Learning Objective: FUN-8.A

Determine a particular solution given a rate vector and initial conditions.

Essential Knowledge: FUN-8.A.1

Methods for calculating integrals of real-valued functions can be extended to parametric or vector-valued functions.

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