This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: xaxis. Your answer should include a sketch of the surface. x = 1 + 2 y 2 , 1 ≤ y ≤ 2 Solution: The curve is rotated about the xaxis, so the equation for surface area is S = Z 2 πy ds . We are given x = 1 + 2 y 2 , so it will be easiest to use ds = p 1 + ( dx/dy ) 2 dy = p 1 + (4 y ) 2 dy = p 1 + 16 y 2 dy . This implies that S = Z 2 πy ds = Z 2 1 2 πy p 1 + 16 y 2 dy . Now use usubstitution: set u = 1 + 16 y 2 , then du = 32 y dy , and so S = Z 2 1 2 πy p 1 + 16 y 2 dy = π 16 Z 65 17 u 1 / 2 du = π 16 · 2 3 u 3 / 2 ﬂ ﬂ ﬂ ﬂ 65 17 = π 24 ‡ 65 √ 6517 √ 17 · . 2 121 3 1 4 2 51 6 7 82 9...
View
Full
Document
This note was uploaded on 09/21/2009 for the course MATH 1234 taught by Professor Egcdd during the Spring '09 term at Aarhus Universitet.
 Spring '09
 EGCDD

Click to edit the document details