2(x + y)i + sin(y) 3. Find the line integral of Faround the perimeter of the rectangle with corners (4, 0), (4, 8), (-2, 8), (-2, 0), traversed in that order. Let F = line integral =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Given the vector field \( \vec{F} = 2(x + y) \, \vec{i} + \sin(y) \, \vec{j} \), find the line integral of \( \vec{F} \) around the perimeter of the rectangle with corners \( (4, 0), (4, 8), (-2, 8), (-2, 0) \), traversed in that order.

**Line Integral:** \(\square\)
Transcribed Image Text:Given the vector field \( \vec{F} = 2(x + y) \, \vec{i} + \sin(y) \, \vec{j} \), find the line integral of \( \vec{F} \) around the perimeter of the rectangle with corners \( (4, 0), (4, 8), (-2, 8), (-2, 0) \), traversed in that order. **Line Integral:** \(\square\)
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