The vector field F = e¯ª i — xe¯ªj is conservative. Find a scalar potential f and evaluate the line integral over any smooth path C connecting A(0, 0) to B(1, 1). f = So FdR=
The vector field F = e¯ª i — xe¯ªj is conservative. Find a scalar potential f and evaluate the line integral over any smooth path C connecting A(0, 0) to B(1, 1). f = So FdR=
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:
The vector field \(\mathbf{F} = e^{-y} \, \mathbf{i} - xe^{-y} \, \mathbf{j}\) is conservative. Find a scalar potential \( f \) and evaluate the line integral over any smooth path \( C \) connecting \( A(0, 0) \) to \( B(1, 1) \).
### Solutions:
1. Find the scalar potential \( f \):
\[
f = \, \underline{\hspace{3cm}}
\]
2. Evaluate the line integral:
\[
\int_C \mathbf{F} \cdot d\mathbf{R} = \, \underline{\hspace{3cm}}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F140bd83b-645e-45c3-8644-e53276eab044%2F2408065c-e56f-471a-9dde-618502bdbe8c%2F8wbhgrj_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem:
The vector field \(\mathbf{F} = e^{-y} \, \mathbf{i} - xe^{-y} \, \mathbf{j}\) is conservative. Find a scalar potential \( f \) and evaluate the line integral over any smooth path \( C \) connecting \( A(0, 0) \) to \( B(1, 1) \).
### Solutions:
1. Find the scalar potential \( f \):
\[
f = \, \underline{\hspace{3cm}}
\]
2. Evaluate the line integral:
\[
\int_C \mathbf{F} \cdot d\mathbf{R} = \, \underline{\hspace{3cm}}
\]
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