Evaluate the line integral by following the given steps. 4xy dx + 2x²y dy C is the triangle with vertices (0,0),(4, 0), and (0, 3). The curve C can split up into each one of its sides (shown in the picture below) Н) L(t) B(t) 4xy dx + 2x²y dy 4хydx + 2x*y dy + 4xy dx + 2x² y dy+ | 4xy dx + 2x²y dy Н Parametrize each side of the triangle B(t) = Σ Σ Σ Н() Σ Σ Σ L(t) = Σ . te Σ Σ (use the most natural parametrizations and remember which direction you need to go)
Evaluate the line integral by following the given steps. 4xy dx + 2x²y dy C is the triangle with vertices (0,0),(4, 0), and (0, 3). The curve C can split up into each one of its sides (shown in the picture below) Н) L(t) B(t) 4xy dx + 2x²y dy 4хydx + 2x*y dy + 4xy dx + 2x² y dy+ | 4xy dx + 2x²y dy Н Parametrize each side of the triangle B(t) = Σ Σ Σ Н() Σ Σ Σ L(t) = Σ . te Σ Σ (use the most natural parametrizations and remember which direction you need to go)
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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Transcribed Image Text:Evaluate the line integral by following the given steps.
4xy dx + 2x²y dy
C is the triangle with vertices (0,0),(4, 0), and (0, 3).
The curve C can split up into each one of its sides (shown in the picture below)
Н)
L(t)
B(t)
4xy dx + 2x²y dy
4хydx + 2x*y dy +
4xy dx + 2x² y dy+ | 4xy dx + 2x²y dy
Н
Parametrize each side of the triangle
B(t) =
Σ
Σ
Σ
Н()
Σ
Σ
Σ
L(t) =
Σ . te
Σ
Σ
(use the most natural parametrizations and remember which direction you need to go)
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