1) Find the area bounded between the curves x =y( y 4) and x = (y 1)(y 3) , by doing the following: a) Sketch the region, including the representative slice that you use. b) Find the limits of integration by hand, showing your steps. c) Write your definite integral, using proper notation. d) Evaluate your integral to find the area (you may use integration technology for the evaluation). 2) Find the exact volume of the solid of revolution generated when the region R bounded by y = 8x , the x-axis, and the lines x = 0 and x = 1 is revolved about the line y = 3. Include a sketch of the region R showing the representative element you choose to use. Integrate and evaluate by hand, showing your steps. 3) Find the exact volume of the solid of revolution generated when the region R bounded by y = sian) and the xaxis between x = 0 and x = IE is revolved about the yaxis. Include a sketch of the region R showing the representative element you choose to use. Integrate and evaluate by hand, showing your steps