2. (a) Given a double integral 1 = over the region R enclosed by the ellipse = 1, where a, b are positive constants, and a > b =0. (i) Sketch the region of integration over the region R in the xy-plane. (ii) Given the coordinate transformation x = au, and y = bv, find the Jacobian of the transformation /(u, v) = (x, y) B(1, v) (iii) Sketch the region in the wv-plane corresponding to the given transformation. Hence, evaluate the double integral in terms of a and b in the inv-plane. (13 marks) (b) Consider the solid region D bounded by y = 0, z = 0, y = x, and z = 2-x*. Sketch the region D in the xyz-space, and evaluate the triple integral (12 marks)