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Question 4 Conservative Vector Fields Consider the vector field F(r, y, 2) (2ry:,3r ys, 4r?y="). (i) Show that F is a conservative vector field and find o such that F = Vộ. (ii) Use this to evaluate F dr, where C consists of the line segment from (1,0,-2) to (1, 1,0) followed by the curve given given by r(t) = (e", cos(t), t) for 0sts1.

Question 4 Conservative Vector Fields Consider the vector field F(r, y, 2) (2ry:,3r ys, 4r?y="). (i) Show that F is a conservative vector field and find o such that F = Vộ. (ii) Use this to evaluate F dr, where C consists of the line segment from (1,0,-2) to (1, 1,0) followed by the curve given given by r(t) = (e", cos(t), t) for 0sts1.

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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Question 4 Conservative Vector Fields Consider the vector field F(r, y, 2) = (2ry+,3r y4, 4r*yz*). (i) Show that F is a conservative vector field and find o such that F = Vộ. (ii) Use this to evaluate F dr, where C consists of the line segment from (1,0, -2) to (1,1,0) followed by the curve given given by r(t) = (e", cos(t), t) for 0sts1.
Transcribed Image Text:Question 4 Conservative Vector Fields Consider the vector field F(r, y, 2) = (2ry+,3r y4, 4r*yz*). (i) Show that F is a conservative vector field and find o such that F = Vộ. (ii) Use this to evaluate F dr, where C consists of the line segment from (1,0, -2) to (1,1,0) followed by the curve given given by r(t) = (e", cos(t), t) for 0sts1.
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