Consider the helicoid parametrized as X(u1, u2) = (u1 cos 3u2, u1 sin 3u2, 5u2), 0 u1 5

Vector Calculus | 4th Edition | ISBN: 9780321780652 | Authors: Susan J. Colley

ISBN: 9780321780652 319

Solution for problem 10 Chapter 8.2

Vector Calculus | 4th Edition

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Problem 10

Consider the helicoid parametrized as X(u1, u2) = (u1 cos 3u2, u1 sin 3u2, 5u2), 0 u1 5, 0 u2 2. Let S denote the underlying surface of the helicoid and let be the orientation 2-form defined in terms of X as X(u1,u2)(a, b) = det 5 sin 3u2 a1 b1 5 cos 3u2 a2 b2 3u1 a3 b3 . (a) Explain why the parametrization X is incompatible with . (b) Modify the parametrization X to one having the same underlying surface S but that is compatible with . (c) Alternatively, modify the orientation 2-form to so that the original parametrization X is compatible with .(d) Calculate S , where = z dx dy (x 2 + y2) dy dz and S is oriented using .

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Chapter 8.2, Problem 10 is Solved

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Textbook: Vector Calculus

Edition: 4

Author: Susan J. Colley

ISBN: 9780321780652

This textbook survival guide was created for the textbook: Vector Calculus, edition: 4. The full step-by-step solution to problem: 10 from chapter: 8.2 was answered by , our top Calculus solution expert on 03/05/18, 06:59PM. Vector Calculus was written by and is associated to the ISBN: 9780321780652. The answer to “Consider the helicoid parametrized as X(u1, u2) = (u1 cos 3u2, u1 sin 3u2, 5u2), 0 u1 5, 0 u2 2. Let S denote the underlying surface of the helicoid and let be the orientation 2-form defined in terms of X as X(u1,u2)(a, b) = det 5 sin 3u2 a1 b1 5 cos 3u2 a2 b2 3u1 a3 b3 . (a) Explain why the parametrization X is incompatible with . (b) Modify the parametrization X to one having the same underlying surface S but that is compatible with . (c) Alternatively, modify the orientation 2-form to so that the original parametrization X is compatible with .(d) Calculate S , where = z dx dy (x 2 + y2) dy dz and S is oriented using .” is broken down into a number of easy to follow steps, and 126 words. Since the solution to 10 from 8.2 chapter was answered, more than 221 students have viewed the full step-by-step answer. This full solution covers the following key subjects: . This expansive textbook survival guide covers 47 chapters, and 1691 solutions.