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19-20 Show that the line integral is independent of path and evaluate the integral. 19. fc 2xe dx + (2y - x²e-¹) dy, C is any path from (1, 0) to (2, 1)

19-20 Show that the line integral is independent of path and evaluate the integral. 19. fc 2xe dx + (2y - x²e-¹) dy, C is any path from (1, 0) to (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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16.3

19 please 

 

C: x = √t, y=t+1, z = t², 0≤t≤1 16. F(x, y, z) = (y²z+ 2xz²)i + 2xyzj + (xy² + 2x²z) k, 17. F(x, y, z) = yze*² i + e*² j + xyek, C: r(t) = (t² + 1) i + (t² − 1)j + (t² - 2t) k, XZ 0≤1≤2 YOVER 117 18. F(x, y, z) = sin y i + (x cos y + cos z) j- y sin z k, C: r(t) = sin ti + tj + 2t k, 0≤t≤ π/2 19-20 Show that the line integral is independent of path and evaluate the integral. 19. 2xe dx + (2y = x²e) dy, C is any path from (1, 0) to (2, 1) SECTION 16.3 The Fundar 20. fc sin y dx + (x cos y − sin y) dy, C is any path from (2, 0) to (1, π) 28. Let F=Vf, w and C₂ that are 21. Suppose you're asked to determine the curve that requires the least work for a force field F to move a particle from one point to another point. You decide to check first whether F is conservative, and indeed it turns out that it is. How would you reply to the request? 22. Suppose an experiment determines that the amount of work required for a force field F to move a particle from the point (1, 2) to the point (5, -3) along a curve C₁ is 1.2 J and the work done by F in moving the particle along another curve C₂ between the same two points is 1.4 J. What can you say about F? Why? 23-24 Find the work done by the force field F in moving an object from P to Q. 23. F(x, y) = x³ i+y³j; P(1, 0), Q(2, 2) 24. F(x, y) = (2x + y) i+xj; P(1, 1), Q(4,3) (a) F. dr JC₁ 29. Show that if conservative derivatives, ap dy 30. Use Exerc cy dx + 31-34 Determ (b) connected 31. {(x, y) | 33. {(x, y) 34. {(x, y) 35. Let F (a) S (b): 36. (a)
Transcribed Image Text:C: x = √t, y=t+1, z = t², 0≤t≤1 16. F(x, y, z) = (y²z+ 2xz²)i + 2xyzj + (xy² + 2x²z) k, 17. F(x, y, z) = yze*² i + e*² j + xyek, C: r(t) = (t² + 1) i + (t² − 1)j + (t² - 2t) k, XZ 0≤1≤2 YOVER 117 18. F(x, y, z) = sin y i + (x cos y + cos z) j- y sin z k, C: r(t) = sin ti + tj + 2t k, 0≤t≤ π/2 19-20 Show that the line integral is independent of path and evaluate the integral. 19. 2xe dx + (2y = x²e) dy, C is any path from (1, 0) to (2, 1) SECTION 16.3 The Fundar 20. fc sin y dx + (x cos y − sin y) dy, C is any path from (2, 0) to (1, π) 28. Let F=Vf, w and C₂ that are 21. Suppose you're asked to determine the curve that requires the least work for a force field F to move a particle from one point to another point. You decide to check first whether F is conservative, and indeed it turns out that it is. How would you reply to the request? 22. Suppose an experiment determines that the amount of work required for a force field F to move a particle from the point (1, 2) to the point (5, -3) along a curve C₁ is 1.2 J and the work done by F in moving the particle along another curve C₂ between the same two points is 1.4 J. What can you say about F? Why? 23-24 Find the work done by the force field F in moving an object from P to Q. 23. F(x, y) = x³ i+y³j; P(1, 0), Q(2, 2) 24. F(x, y) = (2x + y) i+xj; P(1, 1), Q(4,3) (a) F. dr JC₁ 29. Show that if conservative derivatives, ap dy 30. Use Exerc cy dx + 31-34 Determ (b) connected 31. {(x, y) | 33. {(x, y) 34. {(x, y) 35. Let F (a) S (b): 36. (a)
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