Area enclosed by a polar curveAQA A-Level Further Maths: Mind map

Exam questions on Area enclosed by a polar curve

1. A spiral has polar equation $r=2\theta$ for $0\le\theta\le\pi$.
   Find the exact area of the region bounded by the spiral and the half-lines $\theta=\frac{\pi}{2}$ and $\theta=\pi$.2 marks
2. A curve $C$ has polar equation $r=3+2\cos\theta$ for $0\le\theta\le2\pi$.
   Hence find the area enclosed by $C$.2 marks
3. A curve $C$ has polar equation $r=4\sin2\theta$ for $0\le\theta\le\frac{\pi}{2}$, forming one loop from the pole.
   Show that the area enclosed by the loop is $2\pi$.3 marks