Instructions: you have two hours for this examination, you are permitted the use of a one page notes sheet (8. 5x11, both sides), solve each problem in the space provided. Write the letter of your answer in the appropriate space on this. A correct answer with no supporting work may receive little or no credit: each problem is worth 10 points, there are 20 problems; you are to do all of them. Write the letters corresponding to your answers here: Find the average value of the function f (x) = x cos(2x) on the interval 0 ! x ! Find the volume of the solid obtained by rotating the region bounded by the curves y = ex ,! y = 1,! x = 1 about the x-axis. 2 e2 1 e2 1 e2 1. What is the volume of the solid of revolution generated by rotating about the y-axis the region enclosed by the graph of.