A3. (21) Find the volume of the region that lies between z(x, y) : 4- y and the xy plane in region R that is bounded by the parabolas y2 = 4x and x2 : 4y as shown in Figure 3. [12 marks] Figure 3 (b) Plot the graph of the following function where H(t) is the Heaviside function: V(t) =H(t 1)H(4t)+1 [5 marks] (0) Evaluate the following integral: [8 marks] 1 f x5 lnx dx