Area in polar coordinates

Area in polar coordinates Quiz

Spec 7.1 · Edexcel International A Level Further Maths: Quiz

Studying this course? Keep your progress in one place.

Pick an answer for each. Quizzes never use energy.

5 questions, one answer each

Each answer is checked as you go, with why.

See all 5 questions

  1. 1. Which integral gives the area bounded by r=sin⁡2θr=\sin2\theta for 0≤θ≤π20\le\theta\le\frac{\pi}{2}?

    • A. ∫0π/2sin⁡22θ dθ\int_0^{\pi/2}\sin^22\theta\,d\theta
    • B. 12∫0π/2sin⁡2θ dθ\frac12\int_0^{\pi/2}\sin2\theta\,d\theta
    • C. 12∫0π/2sin⁡22θ dθ\frac12\int_0^{\pi/2}\sin^22\theta\,d\theta
    • D. 12∫0π/2sin⁡2θ dθ\frac12\int_0^{\pi/2}\sin^2\theta\,d\theta

  2. 2. Find 12∫0πcos⁡2θ dθ\frac12\int_0^{\pi}\cos^2\theta\,d\theta.

    • A. π2\frac{\pi}{2}
    • B. π4\frac{\pi}{4}
    • C. π\pi
    • D. π8\frac{\pi}{8}

  3. 3. The area enclosed by r=2(1+cos⁡θ)r=2(1+\cos\theta), 0≤θ≤2π0\le\theta\le2\pi, is

    • A. 3π3\pi
    • B. 4π4\pi
    • C. 8π8\pi
    • D. 6π6\pi

  4. 4. The curves r=2r=2 and r=4cos⁡θr=4\cos\theta meet where

    • A. θ=±π3\theta=\pm\frac{\pi}{3}
    • B. θ=±π6\theta=\pm\frac{\pi}{6}
    • C. θ=±π4\theta=\pm\frac{\pi}{4}
    • D. θ=±π2\theta=\pm\frac{\pi}{2}

  5. 5. Why must you expand (1+cos⁡θ)2(1+\cos\theta)^2 before integrating?

    • A. Because ∫(1+cos⁡θ)2 dθ=13(1+cos⁡θ)3\int(1+\cos\theta)^2\,d\theta=\frac13(1+\cos\theta)^3
    • B. Because cos⁡2θ\cos^2\theta needs the double-angle identity to be integrated
    • C. Because rr must be negative
    • D. Because the limits change

Quiz