Instructions: write your complete solutions on this paper. No graphing calculator is allowed to be used. To receive credit, you must show all work. You are not required to simplify your answers. Assume all physical units (length, force, etc. ) are in the mks system, hence are compatible. (1) (20 pts. ) Let c denote the curve y = e x, where 0 x ln 2. In this case, do not evaluate the integrals. (a) the length of c. (b) the area of the surface generated when c is revolved about the (i) x-axis (ii) y-axis. Let r denote the region between the curves y = x2 and y = x1/2. The length of a rope is 75 and the weight is 25. 60 was hanging from a winch down a long shaft and was raised to the top. How much work was done? (4) (10 pts. ) Find the average value of the function f (x) = e x on the interval.