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

Exam questions on Area enclosed by a polar curve

1. The curve $C$ has polar equation $r=2\theta$ for $0\le\theta\le\pi$.
   Find the exact area of the region bounded by $C$ and the half-lines $\theta=\frac{\pi}{2}$ and $\theta=\pi$.2 marks
2. The curve $C$ has polar equation $r=3+2\cos\theta$ for $0\le\theta\le2\pi$.
   Find the exact area of the region bounded by $C$ and the half-lines $\theta=0$ and $\theta=\frac{\pi}{2}$.2 marks
3. The curve $C$ has polar equation $r=2(1+\cos\theta)$ for $0\le\theta\le\pi$.
   Find the polar coordinates of the point of $C$, other than the pole and the point where $\theta=0$, at which the tangent is perpendicular to the initial line.3 marks