2. Verify that the vector field F(x, y) = (2xy + x-3y)i + (x² −3x+y)j is conservative. Then use the fundamental theorem of line integrals to evaluate ›+x− 3y)dx + (x² − 3x + y)dy], [(2xy + where C' is any path from (0,1) to (1,4).
2. Verify that the vector field F(x, y) = (2xy + x-3y)i + (x² −3x+y)j is conservative. Then use the fundamental theorem of line integrals to evaluate ›+x− 3y)dx + (x² − 3x + y)dy], [(2xy + where C' is any path from (0,1) to (1,4).
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
Q4.2
1-17/18
![2. Verify that the vector field
F(x, y) = (2xy + x-3y)i + (x² −3x+y)j
is conservative. Then use the fundamental theorem of line integrals to evaluate
›+x− 3y)dx + (x² − 3x + y)dy],
[(2xy +
where C' is any path from (0,1) to (1,4).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5f5865b5-d389-47d9-88bb-07a7dc29f1b7%2F0f2c8d01-0daa-4fb1-9393-e4d4f0e7215e%2Fqpyivg_processed.png&w=3840&q=75)
Transcribed Image Text:2. Verify that the vector field
F(x, y) = (2xy + x-3y)i + (x² −3x+y)j
is conservative. Then use the fundamental theorem of line integrals to evaluate
›+x− 3y)dx + (x² − 3x + y)dy],
[(2xy +
where C' is any path from (0,1) to (1,4).
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