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
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
Problem 1RQ
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Question
![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
\[
\int_C \mathbf{F} \cdot d\mathbf{r} = \boxed{\phantom{0}}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff35f8f89-65fc-4b90-98e9-68f8eaa1b3da%2Fc0e2fbaa-35a9-48e0-a0c6-49ed609d14b2%2F00mfefd_processed.jpeg&w=3840&q=75)
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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