??? - 2013 Q9
9. Fig. 9 shows the curve with equation y3= x3/2x-1. It has asymptote x=a and turning point P
(i) Write down the value of a. [1]
(ii) Show that
(ii) Show that
Hence find the coordinates of the turning point P, giving the y-coordinate to 3 significant figures. [9]
(iii) Show that the substitution u = 2x-1 transforms
(iii) Show that the substitution u = 2x-1 transforms
Hence find the exact area of the region enclosed by the curve y3= x3/2x-1. the x-axis and the lines x = 1 and x = 4.5 [8]