4) Consider the region R in the half of the -y plane for which x > 0, bounded by the three curves y = x, y = -x² and x

= 1. Give a variable transformation x=x(u, v), \quad y=y(u, v) so that the region in the u-vplane corresponding to R is given by S=\{(u, v) \mid 0 \leq u \leq 1,0 \leq v \leq 1\} Also determine the Jacobian of this variable transformation. Show all working.