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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. C a. -48 b. 96 c. 420-√2 d.-228√2

41. Evaluate the line integral over the given curve C. (9x + 3y)ds; r(t) = (t - 9)i + tj, 0 ≤ t ≤ 4. C a. -48 b. 96 c. 420-√2 d.-228√2

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 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. a. 40 b. 160 3 a. 4л b. 2π c. -87 d. 2π e. None of these 43. Use Green's Theorem to evaluate the line integral along the positively oriented closed curve C. 2xydx + 5x²dy, where C is the triangle with vertices (0, 0), (2, 5) and (0, 5). 80 3 d. 10 +9)/3 (4) √(+ (di C. Copyright Cengage Learning. Powered by Cognero [x²ydx-xy²dy, 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 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. a. 40 b. 160 3 a. 4л b. 2π c. -87 d. 2π e. None of these 43. Use Green's Theorem to evaluate the line integral along the positively oriented closed curve C. 2xydx + 5x²dy, where C is the triangle with vertices (0, 0), (2, 5) and (0, 5). 80 3 d. 10 +9)/3 (4) √(+ (di C. Copyright Cengage Learning. Powered by Cognero [x²ydx-xy²dy, Page 14
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