Compute the line integral of the vector field F = (3y, −3x) over the circle x² + y² = 81 oriented clockwise F. ds =
Compute the line integral of the vector field F = (3y, −3x) over the circle x² + y² = 81 oriented clockwise F. ds =
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
![**Problem Statement:**
Compute the line integral of the vector field **F** = ⟨3y, -3x⟩ over the circle defined by the equation \(x^2 + y^2 = 81\), oriented clockwise.
\[
\int_{C} \mathbf{F} \cdot d\mathbf{s} =
\]
**Details:**
- Vector field **F** is given with components 3y in the x-direction and -3x in the y-direction.
- The path of integration is a circle with radius 9 (since \(\sqrt{81} = 9\)), centered at the origin.
- The orientation for the line integral is clockwise.
**Graph/Diagram Explanation:**
There are no graphs or diagrams provided in this image. The problem primarily involves performing calculations related to the line integral along a circular path with defined vector field properties and orientation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8b731f0-d86e-4c27-b4bf-d8b1bfda93ca%2F3326e291-dc52-408d-b435-06769f8c13e5%2F2w8j67i_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Compute the line integral of the vector field **F** = ⟨3y, -3x⟩ over the circle defined by the equation \(x^2 + y^2 = 81\), oriented clockwise.
\[
\int_{C} \mathbf{F} \cdot d\mathbf{s} =
\]
**Details:**
- Vector field **F** is given with components 3y in the x-direction and -3x in the y-direction.
- The path of integration is a circle with radius 9 (since \(\sqrt{81} = 9\)), centered at the origin.
- The orientation for the line integral is clockwise.
**Graph/Diagram Explanation:**
There are no graphs or diagrams provided in this image. The problem primarily involves performing calculations related to the line integral along a circular path with defined vector field properties and orientation.
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