Consider the vector field F = (x³y¹, x¹y³). O The vector field is not conservative The vector field is conservative, and the potential function for F is (use K for constant) (x, y) - If F is conservative, use ☀(x, y) to evaluate along a simple closed smooth oriented curve [F F.dr S 1.² с (C). F.dr
Consider the vector field F = (x³y¹, x¹y³). O The vector field is not conservative The vector field is conservative, and the potential function for F is (use K for constant) (x, y) - If F is conservative, use ☀(x, y) to evaluate along a simple closed smooth oriented curve [F F.dr S 1.² с (C). F.dr
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
5.4-6
![Consider the vector field \(\vec{F} = \langle x^3 y^4, x^4 y^3 \rangle\).
- ○ The vector field is not conservative.
- ○ The vector field is conservative, and the potential function for \(\vec{F}\) is (use \(K\) for constant)
\[
\phi(x, y) = \underline{\hspace{3cm}}
\]
If \(\vec{F}\) is conservative, use \(\phi(x, y)\) to evaluate \(\int_C \vec{F} \cdot d\vec{r}\) along a simple closed smooth oriented curve \(C\).
\[
\int_C \vec{F} \cdot d\vec{r} = \underline{\hspace{3cm}}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4e39a1d0-143c-41f0-ae59-e967e0535bad%2Fdca35fb3-698b-4336-94c7-e4abebc56417%2F249axmt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the vector field \(\vec{F} = \langle x^3 y^4, x^4 y^3 \rangle\).
- ○ The vector field is not conservative.
- ○ The vector field is conservative, and the potential function for \(\vec{F}\) is (use \(K\) for constant)
\[
\phi(x, y) = \underline{\hspace{3cm}}
\]
If \(\vec{F}\) is conservative, use \(\phi(x, y)\) to evaluate \(\int_C \vec{F} \cdot d\vec{r}\) along a simple closed smooth oriented curve \(C\).
\[
\int_C \vec{F} \cdot d\vec{r} = \underline{\hspace{3cm}}
\]
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