Suppose Vf(x, y) = 3y sin(xy)i + 3x sin(xy)], F = ▼ ƒ(x, y), and C is the segment of the parabola y = 2x² from the point (1, 2) to (5, 50). Then LE F·dr = 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Suppose \( \nabla f(x, y) = 3y \sin(xy) \mathbf{i} + 3x \sin(xy) \mathbf{j} \),

\( \mathbf{F} = \nabla f(x, y) \), and \( C \) is the segment of the parabola \( y = 2x^2 \) from the point \( (1, 2) \) to \( (5, 50) \). Then

\[
\int_C \mathbf{F} \cdot d\mathbf{r} = \boxed{\phantom{0}}
\]
Transcribed Image Text:Suppose \( \nabla f(x, y) = 3y \sin(xy) \mathbf{i} + 3x \sin(xy) \mathbf{j} \), \( \mathbf{F} = \nabla f(x, y) \), and \( C \) is the segment of the parabola \( y = 2x^2 \) from the point \( (1, 2) \) to \( (5, 50) \). Then \[ \int_C \mathbf{F} \cdot d\mathbf{r} = \boxed{\phantom{0}} \]
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