GROUP WORK 1, SECTION 8.2 Gabriel's Horn 1tox00. (Okay, you don't actually have to graph it all the way out to infinity.) 2. Now think of the object formed by rotating this curve about the x-axis. This object is called Gabriel's Horm. Your job is to paint Gabriel's Horm. You are given a brush and as many cans of paint as you want. But before you start, it occurs to you that you might be wasting your time. After all, the hon is unbounded. You don't want to spend hours and hours on a job that might never be finished! Here's an idea: calculate the volume of Gabriel's Hom. That is, find the volume for the solid obtained by rotating the region bounded by f (x)-1/x, x = 1, and y-0 about the x-axis. If this volume is finite, you could fill the horm with paint, shake it around a litle, pour out the extra and be done with the job. (You are allowed to waste paint in Heaven.) So, can you paint the horn?