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, у) 3< ху + 1, х* + 2у >. Use these parametrizations for the two line segments: ri (1) =< 2 – t, t>, r2 (t) =< 0, 2 – t >, 0

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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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