19. Use Stoke's theorem to evaluate the line integral [(1 + y)z dx + (1+z)x dy + (1 + x)y dz] for the given closed path C. (a) C is the boundary of the standard unit circle in the xy-plane. (b) C is the boundary of the triangle with vertices (1, 0, 0), (0, 1, 0), (0, 0, 1).
19. Use Stoke's theorem to evaluate the line integral [(1 + y)z dx + (1+z)x dy + (1 + x)y dz] for the given closed path C. (a) C is the boundary of the standard unit circle in the xy-plane. (b) C is the boundary of the triangle with vertices (1, 0, 0), (0, 1, 0), (0, 0, 1).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![19. Use Stoke's theorem to evaluate the line integral
f [(1 + y)z dæ + (1+z)æ dy + (1 + x)y dz]
for the given closed path C.
(a) C is the boundary of the standard unit circle in the xy-plane.
(b) C is the boundary of the triangle with vertices (1, 0, 0), (0, 1, 0), (0, 0, 1).
(c) C is the elliptic path x = 2 cos 0, y = sin 0, z = 1 for 0 ≤ 0 ≤ 2T.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa36b69c8-3a83-4af0-8d9b-af1f42f9d145%2F9aa23b18-2f5c-49b6-8dcf-19e56a01d4e9%2Frf60pst_processed.jpeg&w=3840&q=75)
Transcribed Image Text:19. Use Stoke's theorem to evaluate the line integral
f [(1 + y)z dæ + (1+z)æ dy + (1 + x)y dz]
for the given closed path C.
(a) C is the boundary of the standard unit circle in the xy-plane.
(b) C is the boundary of the triangle with vertices (1, 0, 0), (0, 1, 0), (0, 0, 1).
(c) C is the elliptic path x = 2 cos 0, y = sin 0, z = 1 for 0 ≤ 0 ≤ 2T.
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