Concept explainers
Explain why or why not 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.
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