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42. Use Green's Theorem and or a computer algebra system to evaluate [x²ydx-xy²dy, where C is the circle x² + y²=4 with counterclockwise orientation. a. 4x b. 2x c.-8.r d. 2x e. None of these

42. Use Green's Theorem and or a computer algebra system to evaluate [x²ydx-xy²dy, where C is the circle x² + y²=4 with counterclockwise orientation. a. 4x b. 2x c.-8.r d. 2x e. None of these

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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41. Evaluate the line integral over the given curve C. (9x + 3y)ds; r(t) = (t - 9)i + tj, 0 ≤ t ≤ 4. a. -48 b. 96 c. 420√2 C. d.-228√/2 42. Use Green's Theorem and/or a computer algebra system to evaluate where C is the circle x² + y² =4 with counterclockwise orientation. e [x²ydx-xy²dy, a. 4x b. 2x с. -8л d. 2x e. None of these 43. Use Green's Theorem to evaluate the line integral along the positively oriented closed curve C. $2xydx + 5x dy, where C is the triangle with vertices (0, 0), (2, 5) and (0, 5). a. 40 b. 160 3 c. 800 3 d. 10 X Page 14
Transcribed Image Text:41. Evaluate the line integral over the given curve C. (9x + 3y)ds; r(t) = (t - 9)i + tj, 0 ≤ t ≤ 4. a. -48 b. 96 c. 420√2 C. d.-228√/2 42. Use Green's Theorem and/or a computer algebra system to evaluate where C is the circle x² + y² =4 with counterclockwise orientation. e [x²ydx-xy²dy, a. 4x b. 2x с. -8л d. 2x e. None of these 43. Use Green's Theorem to evaluate the line integral along the positively oriented closed curve C. $2xydx + 5x dy, where C is the triangle with vertices (0, 0), (2, 5) and (0, 5). a. 40 b. 160 3 c. 800 3 d. 10 X Page 14
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