Area enclosed by a polar curve

Area enclosed by a polar curve Quiz

Spec 7.3 · Edexcel A-Level Further Maths: Quiz

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  1. 1. Find the area enclosed by r=3r=3 between θ=0\theta=0 and θ=π3\theta=\frac{\pi}{3}.

    • A. 3π3\pi
    • B. 3π2\frac{3\pi}{2}
    • C. 9π2\frac{9\pi}{2}
    • D. π2\frac{\pi}{2}

  2. 2. Find the area enclosed by the cardioid r=1+cos⁡θr=1+\cos\theta, 0≤θ≤2π0\le\theta\le2\pi.

    • A. 3π2\frac{3\pi}{2}
    • B. 3π3\pi
    • C. π\pi
    • D. 2π2\pi

  3. 3. A tangent is perpendicular to the initial line where

    • A. dydθ=0\frac{dy}{d\theta}=0
    • B. drdθ=0\frac{dr}{d\theta}=0
    • C. r=0r=0
    • D. dxdθ=0\frac{dx}{d\theta}=0

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

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

  5. 5. For r=2cos⁡θr=2\cos\theta with 0<θ<π20<\theta<\frac{\pi}{2}, the tangent is parallel to the initial line when θ=\theta=

    • A. π6\frac{\pi}{6}
    • B. π4\frac{\pi}{4}
    • C. π3\frac{\pi}{3}
    • D. π2\frac{\pi}{2}

Quiz