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Consider the following vector field: F = (y* + 1, 3ry + 1). (8.1) Is ſ. F · dr path-independent? Justify your answer clearly. (8.2) Show that ſF · dr = 2, where C is the semi-circular path, in the first quadrant, with starting point (0,0) and terminal point (2, 0).

Consider the following vector field: F = (y* + 1, 3ry + 1). (8.1) Is ſ. F · dr path-independent? Justify your answer clearly. (8.2) Show that ſF · dr = 2, where C is the semi-circular path, in the first quadrant, with starting point (0,0) and terminal point (2, 0).

Advanced Engineering Mathematics
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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Consider the following vector field: F = (y* + 1, 3ry² + 1). (8.1) Is fe F· dr path-independent? Justify your answer clearly. (8.2) Show that S¢F•dr = 2, where C is the semi-circular path, in the first quadrant, with starting point (0, 0) and terminal point (2,0).
Transcribed Image Text:Consider the following vector field: F = (y* + 1, 3ry² + 1). (8.1) Is fe F· dr path-independent? Justify your answer clearly. (8.2) Show that S¢F•dr = 2, where C is the semi-circular path, in the first quadrant, with starting point (0, 0) and terminal point (2,0).
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