Compute the circulation of F(x, y) = − 27 – 5j along the line segment C' from (- 3, — 4) to (1, 0). • The circulation is F. dr C =
Compute the circulation of F(x, y) = − 27 – 5j along the line segment C' from (- 3, — 4) to (1, 0). • The circulation is F. dr C =
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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![**Problem Statement:**
Compute the circulation of \( \vec{F}(x, y) = -2\vec{i} - 5\vec{j} \) along the line segment \( C \) from \((-3, -4)\) to \((1, 0)\).
**Graph Description:**
- The graph is a vector field showing vectors \( \vec{F}(x, y) = -2\vec{i} - 5\vec{j} \).
- A grid from -5 to 5 on both x and y axes is presented.
- Each grid point contains a blue vector pointing generally southwest, consistent with the vector \(-2\vec{i} - 5\vec{j}\).
- A red line segment connects the point \((-3, -4)\) to the point \((1, 0)\), indicating the path \( C \).
- The endpoints of the line segment are highlighted with yellow circles.
**Calculation:**
To find the circulation of \( \vec{F} \) along the curve \( C \), the integral is set up as:
\[
\int_C \vec{F} \cdot d\vec{r} =
\]
**Conclusion:**
The formula represents the circulation of the vector field along the specified path. Evaluation of this integral would provide the measurement of how much the field circulates around the path \( C \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F442a294d-0278-4659-8cf9-c6ac571e9e15%2F3fb8d5b1-d15c-41a5-a19c-02090f48a74f%2Fhlgx7v6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Compute the circulation of \( \vec{F}(x, y) = -2\vec{i} - 5\vec{j} \) along the line segment \( C \) from \((-3, -4)\) to \((1, 0)\).
**Graph Description:**
- The graph is a vector field showing vectors \( \vec{F}(x, y) = -2\vec{i} - 5\vec{j} \).
- A grid from -5 to 5 on both x and y axes is presented.
- Each grid point contains a blue vector pointing generally southwest, consistent with the vector \(-2\vec{i} - 5\vec{j}\).
- A red line segment connects the point \((-3, -4)\) to the point \((1, 0)\), indicating the path \( C \).
- The endpoints of the line segment are highlighted with yellow circles.
**Calculation:**
To find the circulation of \( \vec{F} \) along the curve \( C \), the integral is set up as:
\[
\int_C \vec{F} \cdot d\vec{r} =
\]
**Conclusion:**
The formula represents the circulation of the vector field along the specified path. Evaluation of this integral would provide the measurement of how much the field circulates around the path \( C \).
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