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1. sketch the solid formed by revolving the region bounded by y=1/x and y=0 for

ID: 2837885 • Letter: 1

Question

1. sketch the solid formed by revolving the region bounded by y=1/x and y=0 for x>=1 around the x-axis. this solid is known as Gabriel's Horn.

2. Find the volume of Gabriel's Horn (evaluate an improper integral). You must show woek by "slicing" the solid and finding the volume of each "slice"

3. Show that the surface area of Gabriel's Horn is infinite (i.e. the improper integral diverges to infinity). You must show work by "slicing" the solid and finding the outer surface area of each slice.

Note: This problem shows that it is possible to fill in the horn with paint, but impossible to paint it. (chapter 8.2)

Explanation / Answer

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