Explain why or why not Determine whether the

Chapter 6, Problem 21

(choose chapter or problem)

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. a. If the curve y = f 1x2 on the interval 3a, b4 is revolved about the y-axis, the area of the surface generated is L f 1b2 f 1a2 2p f 1y221 + f _1y22 dy. b. If f is not one-to-one on the interval 3a, b4, then the area of the surface generated when the graph of f on 3a, b4 is revolved about the x-axis is not defined. c. Let f 1x2 = 12x2. The area of the surface generated when the graph of f on 3-4, 44 is revolved about the x-axis is twice the area of the surface generated when the graph of f on 30, 44 is revolved about the x-axis. d. Let f 1x2 = 12x2. The area of the surface generated when the graph of f on 3-4, 44 is revolved about the y-axis is twice the area of the surface generated when the graph of f on 30, 44 is revolved about the y-axis.