Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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**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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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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