(a) Consider the functions f, g : R R defined by the expressions f(x) = -10a? + 60r 50 and g(x) = 6x x2. Find 40F 20 4. -20 -40 --10 (x2 - 6x+5) -100 -(x-6) x Figure 1: Plot of the two quadratics. (i) the area under f(r) and above y = 0; (2 marks) (ii) the area under g(x) and above y = 0; (2 marks) (ii) points ri < r2 where f(x) and g(1) intersect; (4 marks) (iv) the area between f(x) and g(x). (4 marks) (b) For the following improper integral 27re-3" dr (1) Identify the type of the integral; (4 marks) (ii) If convergent, find the value of the integral. (4 marks)