**??? - 2013 Q9**

9. Fig. 9 shows the curve with equation

*y*=^{3}*x*^{3}/2*x*-1. It has asymptote*x*=*a*and turning point P(i) Write down the value of

(ii) Show that

*a*. [1]

(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

(iii) Show that the substitution

*u*=*2x*-1 transformsHence find the exact area of the region enclosed by the curve

*y*=^{3}*x*^{3}/2*x*-1. the*x*-axis and the lines*x*= 1 and*x*= 4.5 [8]