Consider the region R in the x-y plane bounded by the three curves y = x, y = -x² and x=1. Give a variable transformation x = x(u, v), y = y(u, v), so that the region in the u-v plane corresponding to R is given by S={(u, v)|0<u≤ 1,0≤ v≤ 1}. Also determine the Jacobian of this variable transformation.