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6. Consider the vector field defined by y F = (²) ² + ( 3y² m (x) - ₂ √ √ ) ³ + ( √T)k i j (a) Use the component test to show that the vector field F is conservative. (b) Find a potential function for F. Show the steps of your computation for this. A

6. Consider the vector field defined by y F = (²) ² + ( 3y² m (x) - ₂ √ √ ) ³ + ( √T)k i j (a) Use the component test to show that the vector field F is conservative. (b) Find a potential function for F. Show the steps of your computation for this. A

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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6. Consider the vector field defined by y F = (²) ² + ( 3y² m (x) - ₂ √ √ ) ³ + ( √T)k i j (a) Use the component test to show that the vector field F is conservative. (b) Find a potential function for F. Show the steps of your computation for this. A
Transcribed Image Text:6. Consider the vector field defined by y F = (²) ² + ( 3y² m (x) - ₂ √ √ ) ³ + ( √T)k i j (a) Use the component test to show that the vector field F is conservative. (b) Find a potential function for F. Show the steps of your computation for this. A
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(c) Using the answers above, compute the value of the line integral -(2,4,5)/y³ 2 [220) (1²) de + (36³²ln(x) - 2 √5) dy + (√) dz
Transcribed Image Text:(c) Using the answers above, compute the value of the line integral -(2,4,5)/y³ 2 [220) (1²) de + (36³²ln(x) - 2 √5) dy + (√) dz
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