Question 5

a. (i) Evaluate $\iint r^3\,dr\,d\theta$ over the area bounded between the circles $r = 2\cos\theta$ and $r = 4\cos\theta$.
(ii) Find the area enclosed by the pair of curves $y = 2 - x$ and $y^2 = 2(2 - x)$. (3 marks)

b. Change the order of integration and hence evaluate the value of the integral $\displaystyle\int_0^{4a}\int_{x^2/4a}^{2\sqrt{ax}} dx\,dy$. (2 marks)