Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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
\[
\int_C \mathbf{F} \cdot d\mathbf{r} = \boxed{\phantom{0}}
\]](https://content.bartleby.com/qna-images/question/f35f8f89-65fc-4b90-98e9-68f8eaa1b3da/c0e2fbaa-35a9-48e0-a0c6-49ed609d14b2/00mfefd_processed.jpeg)
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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