Area enclosed by a polar curve

Area enclosed by a polar curve Quiz

Spec G3 · AQA A-Level Further Maths: Quiz

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  1. 1. Find the area bounded by r=θr=\theta and the half-lines θ=0\theta=0 and θ=π2\theta=\frac{\pi}{2}.

    • A. π324\frac{\pi^3}{24}
    • B. π28\frac{\pi^2}{8}
    • C. π348\frac{\pi^3}{48}
    • D. π312\frac{\pi^3}{12}

  2. 2. Find the area enclosed by r=2r=2 for 0≤θ≤π20\le\theta\le\frac{\pi}{2}.

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

  3. 3. Find the area enclosed by the circle r=4cos⁡θr=4\cos\theta for −π2≤θ≤π2-\frac{\pi}{2}\le\theta\le\frac{\pi}{2}.

    • A. 8π8\pi
    • B. 16π16\pi
    • C. 2π2\pi
    • D. 4π4\pi

  4. 4. Find the area enclosed by the cardioid r=2(1+cos⁡θ)r=2(1+\cos\theta) for 0≤θ≤2π0\le\theta\le2\pi.

    • A. 3π3\pi
    • B. 6π6\pi
    • C. 12π12\pi
    • D. 4π4\pi

  5. 5. The curves r=2r=2 and r=4sin⁡θr=4\sin\theta meet for 0≤θ≤π0\le\theta\le\pi. Which values of θ\theta are the points of intersection?

    • A. π3\frac{\pi}{3} and 2π3\frac{2\pi}{3}
    • B. π4\frac{\pi}{4} and 3π4\frac{3\pi}{4}
    • C. π6\frac{\pi}{6} and 5π6\frac{5\pi}{6}
    • D. π6\frac{\pi}{6} only

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