1. Use Green's Theorem to evaluate the line integral along the given positively oriented curve. a) [xy²dx + 2x²y dy C is the triangle with vertices (0,0), (2,2), and (2,4) b) [(y + eve) dx + (2x + cos y²) dy C is the boundary of the region enclosed by the parabolas y = x² and x = y² √y ³ y³ dx - x³ dy C is the circle x² + y² = 4 c)
1. Use Green's Theorem to evaluate the line integral along the given positively oriented curve. a) [xy²dx + 2x²y dy C is the triangle with vertices (0,0), (2,2), and (2,4) b) [(y + eve) dx + (2x + cos y²) dy C is the boundary of the region enclosed by the parabolas y = x² and x = y² √y ³ y³ dx - x³ dy C is the circle x² + y² = 4 c)
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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show full & complete procedure HANDWRITTEN only. Please answer parts a), b) & c). Note they are subparts of the same question
Transcribed Image Text:1. Use Green's Theorem to evaluate the line integral along the given positively oriented curve.
a) [xy²dx + 2x²y dy
C is the triangle with vertices (0,0), (2,2), and (2,4)
b) [(y + eve) dx + (2x + cos y²) dy
C is the boundary of the region enclosed by the parabolas y = x² and x = y²
√y ³
y³ dx - x³ dy
C is the circle x² + y² = 4
c)
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