Let S be the area of the region R bounded by the curve y = x and the curve y = ax (0 < a < 1), and let S be the area of the region R2 bounded by the curve y = x, the curve y = ax (0 < a < 1), and the line x = 1, where a is the same constant for R1 and R2. (1) (10 points) Find the value of a that minimizes the value of S + S2. What is the minimal value of S + S2? (Hint: You may draw the figures of S1 and S2 for a = 0, 1, 1 to see how they look like.) (2) (10 points) We denote by R the region to be R U R when a = 1. Find the volume of the solid generated by revolving the region R about the line x = -30.