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5. Given the vector field F = (2y – 4x – 2) i + (2x – 2y) 3 (a) Show that the vector field is a gradient vector field. F (b) Find the potential function for the given vector field. (c) Evaluate the integral S, Fdrwhere L is any curve connecting the points A = (-1, 2) and В 3 (2, 1)

5. Given the vector field F = (2y – 4x – 2) i + (2x – 2y) 3 (a) Show that the vector field is a gradient vector field. F (b) Find the potential function for the given vector field. (c) Evaluate the integral S, Fdrwhere L is any curve connecting the points A = (-1, 2) and В 3 (2, 1)

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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5. Given the vector field F (2у — 4г — 2) і + (2 — 2у) 5 (a) Show that the vector field is a gradient vector field. F (b) Find the potential function for the given vector field. (c) Evaluate the integral , Fdrwhere L is any curve connecting the points A = (-1, 2) and В %3 (2, 1) (d) What is the value of fc Fdr where C is a closed curve.
Transcribed Image Text:5. Given the vector field F (2у — 4г — 2) і + (2 — 2у) 5 (a) Show that the vector field is a gradient vector field. F (b) Find the potential function for the given vector field. (c) Evaluate the integral , Fdrwhere L is any curve connecting the points A = (-1, 2) and В %3 (2, 1) (d) What is the value of fc Fdr where C is a closed curve.
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