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If 0≤f(x)≤g(x) for x in the interval [a, b],can the surface obtained by rotating the graph...

If 0≤f(x)≤g(x) for x in the interval [a, b],can the surface obtained by rotating the graph of y=g(x) around the x-axis over the interval have less surface area than the surface obtained by rotating the graph of y=f(x) around the x-axis over the same interval?

I have heard yes and also no so I would like some clarification. Thanks

Math   Calculus   
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Answer #1

NOT TRUE IN GENERAL, as explained through a counterexample below.

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