Calculate the line integral , F · dr, where C is the straight-line path from (2,0) to (0,2), followed by the straight-line path from (0,2) to (0,0), and F is the vector field F (x, y) =< xy + 1, x² + 2y >. Use these parametrizations for the two line segments: ri (t) =< 2 – t, t >, r2 (t) =< 0, 2 – t >, 0

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Calculate the line integral , F · dr, where C is the straight-line path from (2,0) to
(0,2), followed by the straight-line path from (0,2) to (0,0), and F is the vector field
F (x, y) =< xy + 1, x² + 2y>.
Use these parametrizations for the two line segments:
ri (t) =< 2 – t, t >, r2 (t) =< 0, 2 – t >, 0 <t < 2.
-4/3
2/3
O 4/3
-2/3
Transcribed Image Text:Calculate the line integral , F · dr, where C is the straight-line path from (2,0) to (0,2), followed by the straight-line path from (0,2) to (0,0), and F is the vector field F (x, y) =< xy + 1, x² + 2y>. Use these parametrizations for the two line segments: ri (t) =< 2 – t, t >, r2 (t) =< 0, 2 – t >, 0 <t < 2. -4/3 2/3 O 4/3 -2/3
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