Homework SourseIf the region R x y x 1 0 y 1x is rotated about the xaxi
If the region
R= {(x, y) | x ? 1, 0 ? y ? 1/x}
is rotated about the x-axis, the volume of the resulting solid is finite. Determine the surface area. (The surface is shown in the figure and is known as Gabriel\'s horn.)
R= {(x, y) | x ? 1, 0 ? y ? 1/x}
is rotated about the x-axis, the volume of the resulting solid is finite. Determine the surface area. (The surface is shown in the figure and is known as Gabriel\'s horn.)
Solution
The surface area is infinite. It can be proved by comparing it to a smaller integral. Take a look at my source for this comparison.
