Problem 27 Easy Difficulty

If the region $ \Re = \{(x, y) \mid x \ge 1 , 0 \le y \le \frac{1}{x}\} $ is rotated about the x-axis, the volume of the resulting solid is finite (see Exercise 7.8.63). Show that the surface area is infinite. (The surface is shown in the figure and is known as Gabriel's horn.)

Answer

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Video Transcript

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