AP®︎ Calculus BC: Topic 6.11 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 6.11 of AP Calculus BC – Integrating Using Integration by Parts.

Questions List

Topic 6.11

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Q11

Question 1 Easy

To evaluate ∫xcos⁡x dx\int x\cos x\,dx by parts, a student chooses u=xu=x and dv=cos⁡x dxdv=\cos x\,dx. Which expression is equal to ∫xcos⁡x dx\int x\cos x\,dx?

A−xsin⁡x+∫sin⁡x dx-x\sin x+\int\sin x\,dx
Bxsin⁡x+∫sin⁡x dxx\sin x+\int\sin x\,dx
Cxsin⁡x−∫sin⁡x dxx\sin x-\int\sin x\,dx
D−xsin⁡x−∫sin⁡x dx-x\sin x-\int\sin x\,dx

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 6.11: Integrating Using Integration by Parts

Learning Objective: FUN-6.E

For integrands requiring integration by parts: (a) Determine indefinite integrals. (b) Evaluate definite integrals.

Essential Knowledge: FUN-6.E.1

Integration by parts is a technique for finding antiderivatives.

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