Chapter 2.3, Problem 164E

Consider the function y=f(x), which decreases from f(0)=b to f(1) = 0. Set up the integrals for determining the volume, using both the shell method and the disk method, of the solid generated when this region, with x = 0 and y = 0,is rotated around the y-axis. Prove that both methods approximate the same volume. Which method is easier to apply? (Hint: Since f(x) is one-to-one, there exists an inverse f-1 (y).)