AP®︎ Calculus BC: Topic 9.9 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 9.9 of AP Calculus BC – Finding the Area of the Region Bounded by Two Polar Curves.

Questions List

Topic 9.9

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Question 1 Easy

Figure

Region RR is inside r=4sin⁡θr=4\sin\theta and outside r=2r=2. Which integral gives the area of RR?

A12∫π/65π/6(4sin⁡θ−2)2 dθ\displaystyle \frac12\int_{\pi/6}^{5\pi/6}\left(4\sin\theta-2\right)^2\,d\theta
B12∫π/65π/6((4sin⁡θ)2−22) dθ\displaystyle \frac12\int_{\pi/6}^{5\pi/6}\left((4\sin\theta)^2-2^2\right)\,d\theta
C∫π/65π/6((4sin⁡θ)2−22) dθ\displaystyle \int_{\pi/6}^{5\pi/6}\left((4\sin\theta)^2-2^2\right)\,d\theta
D12∫π/65π/6(22−(4sin⁡θ)2) dθ\displaystyle \frac12\int_{\pi/6}^{5\pi/6}\left(2^2-(4\sin\theta)^2\right)\,d\theta

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 9.9: Finding the Area of the Region Bounded by Two Polar Curves

Learning Objective: CHA-5.D

Calculate areas of regions defined by polar curves using definite integrals.

Essential Knowledge: CHA-5.D.2

Areas of regions bounded by polar curves can be calculated with definite integrals.

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