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et F(x, y) = (y sin x)i - 3x²j. et D be the unit square (i.e. D = {(x, y): 0≤x≤ 1,0 ≤ y ≤ 1}), and let C be urve that traces the perimeter of D in a counterclockwise direction. Which of th ollowing is correct?

et F(x, y) = (y sin x)i - 3x²j. et D be the unit square (i.e. D = {(x, y): 0≤x≤ 1,0 ≤ y ≤ 1}), and let C be urve that traces the perimeter of D in a counterclockwise direction. Which of th ollowing is correct?

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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can you help me with these two

4. Let F(x, y) = (y sin x)i - 3x²j. Let D be the unit square (i.e. D = {(x, y): 0 ≤ x ≤ 1,0 ≤ y ≤ 1}), and let C be a curve that traces the perimeter of D in a counterclockwise direction. Which of the following is correct? (a) L.F. F.dr = (b) Jo r = [₁₂₁ F. dr = (d) f = 1₁ yº D (y sin x - 3x²) dA. (c) √ F. dr = f (si y cos z dA. F.dr = (sin x + 6x) dA. -J₂²- (-6x sin æ) dA. (e) None of the other choices. 5. True or False? If C is a closed curve and f(x, y) is a scalar function with continuous partial derivatives on C, then Vf. dr = 0. (a) True. (b) False.
Transcribed Image Text:4. Let F(x, y) = (y sin x)i - 3x²j. Let D be the unit square (i.e. D = {(x, y): 0 ≤ x ≤ 1,0 ≤ y ≤ 1}), and let C be a curve that traces the perimeter of D in a counterclockwise direction. Which of the following is correct? (a) L.F. F.dr = (b) Jo r = [₁₂₁ F. dr = (d) f = 1₁ yº D (y sin x - 3x²) dA. (c) √ F. dr = f (si y cos z dA. F.dr = (sin x + 6x) dA. -J₂²- (-6x sin æ) dA. (e) None of the other choices. 5. True or False? If C is a closed curve and f(x, y) is a scalar function with continuous partial derivatives on C, then Vf. dr = 0. (a) True. (b) False.
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