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Numerade Educator



Problem 63 Hard Difficulty

We know from Example 1 that the region $ \Re = \{ (x, y) \mid x \ge 1, 0 \le y \le \frac{1}{x} \} $ has infinite area. Show that by rotating $ \Re $ about the x-axis we obtain a solid with finite volume.




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Video Transcript

Lucas this region We need to show that by rotating this region about axe access on with the battalion solid with finite volume. If I write way is the volume off? Is this true regional state irritated about X axis? And for each axe area of the section of this What solid if Iko too. So is a disc area off this section. Is he going to pie Times one over X square. This is the area. I was a section here. So the volume as Iko too integral from one to infinity. Off area with this section. Yaks. Now about that mission This's vehicle to the limit. A goes to infinity into girl from one, eh? Hi, moms. One over X squared? Yeah, they're asleep. We come to the limit. A toast to unity. And this is what? Negative. Hi. One over X from one too, eh? This is the limit. A toast to unity makes you a pie bond Over a minus one on one A goes to infinity One hour a goes to zero. So the volume off this solid if we goto Hi. It is a finite volume