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1 S = 1 + dx y dx = 2n ---Select--- v 1 + 1 dx x + 1 00 = 2n dx ---Select--- v Rather than trying to evaluate this integral, note the following. V x4 + 1 ? v Vx4 = x for x > 0 Thus, if the area is finite, we have the following. x4 + 1 o y2 dx = 2n S = 2n dx ? v 2n dx /1 Ji But we know that this integral ---Select--- v so the area S is infinite. 118

1 S = 1 + dx y dx = 2n ---Select--- v 1 + 1 dx x + 1 00 = 2n dx ---Select--- v Rather than trying to evaluate this integral, note the following. V x4 + 1 ? v Vx4 = x for x > 0 Thus, if the area is finite, we have the following. x4 + 1 o y2 dx = 2n S = 2n dx ? v 2n dx /1 Ji But we know that this integral ---Select--- v so the area S is infinite. 118

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.3: Cylinders And Cones
Problem 6E: Suppose that r=12 cm and h=15 cm in the right circular cylinder. Find the exact and approximate a...
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The surface formed by rotating the curve y = , x 2 1, about the x-axis is known as Gabriel's horn. Show that the surface area is infinite (although the enclosed volume is finite). 2 dy 1 + dx S = dx ---Select--- v 1 + 1 dx = 2n x* + 1 = 2n dx ---Select--- v Rather than trying to evaluate this integral, note the following. Vx4 + 1 ? v X4 = x2 for x > 0
Transcribed Image Text:The surface formed by rotating the curve y = , x 2 1, about the x-axis is known as Gabriel's horn. Show that the surface area is infinite (although the enclosed volume is finite). 2 dy 1 + dx S = dx ---Select--- v 1 + 1 dx = 2n x* + 1 = 2n dx ---Select--- v Rather than trying to evaluate this integral, note the following. Vx4 + 1 ? v X4 = x2 for x > 0
y =- 1 dy 1 + dx %3D dx 1 ---Select--- 1 + dx %3D x4 4 + 1 = 2n dx ---Select--- v Rather than trying to evaluate this integral, note the following. Vx4 + 1 ? v 4 = x2 for x > 0 Thus, if the area is finite, we have the following. x* + 1 o x2 dx = 2m S = 2n dx ? v 2TT dx %3D But we know that this integral --Select--- ▼ so the area S is infinite.
Transcribed Image Text:y =- 1 dy 1 + dx %3D dx 1 ---Select--- 1 + dx %3D x4 4 + 1 = 2n dx ---Select--- v Rather than trying to evaluate this integral, note the following. Vx4 + 1 ? v 4 = x2 for x > 0 Thus, if the area is finite, we have the following. x* + 1 o x2 dx = 2m S = 2n dx ? v 2TT dx %3D But we know that this integral --Select--- ▼ so the area S is infinite.
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