QUESTION 2 [TOTAL: 20 MARKS] (a) The figure below shows the graph of the curve with equation y = (x - a)(x - b)* where a and b are positive constants. The shaded region R is bounded by the curve and the x axis. By using integration by parts or other integration method, show that the shaded area is R = (a - b). [5 marks] y=(x-al(x-b)* R O (b) Prooflog. 36 + =log.256 - 2log-48 = -log, 4. [5 marks] (c) The points A and C have coordinates (1, 2) and (5, 6), respectively. (1) Find the coordinate of the point, B, divides the line segment joining points A and C with the ratio 1 :3. [5 marks] (ii) Find the equation of the line perpendicular to the line joining points A and C through point B. [5 marks]