Determine whether the following statements are true and give an explanation or counterexample. 

a. If the curve y = f(x) on the interval [a, b] is revolved about the y-axis, the area of the surface generated is

b. If f is not one-to-one on the interval [a, b], then the area of the surface generated when the graph of f on [a, b] is revolved about the x-axis is not defined.

c. Let f(x) = 12x². The area of the surface generated when the graph of f on [-4, 4] is revolved about the x-axis is twice the area of the surface generated when the graph of f on [0, 4] is revolved about the x-axis.

d. Let f(x) = 12x². The area of the surface generated when the graph of f on [-4, 4] is revolved about the y-axis is twice the area of the surface generated when the graph of f on [0, 4] is revolved about the y-axis.

Transcribed Image Text:

ef(b) 2mf(y) V1 + f'(v)² dy. f(a)