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Suppose F(x, y) = (4x + 2y)i + (2x + 4y)j. Evaluate the line integral for each of the given paths, which are comprised of line segments and arcs of circles. (a) If C is the open semicircular path in figure I of radius. 2 oriented counterclockwise, then Ja F. dr= (b) If C is the open piecewise linear path in figure II from (2, 0) to (0, -2) to (-2, 0), then [..F.. F.dr = (c) If C is the closed path in figure III along the boundary of a semi-disk of radius 2 oriented counterclockwise, then L.F. dr = √√2/2 -1 1 1 " -3 -4 1 -3 -1 || 2 4 -3 -4 -2 -1 ||| 1 3

Suppose F(x, y) = (4x + 2y)i + (2x + 4y)j. Evaluate the line integral for each of the given paths, which are comprised of line segments and arcs of circles. (a) If C is the open semicircular path in figure I of radius. 2 oriented counterclockwise, then Ja F. dr= (b) If C is the open piecewise linear path in figure II from (2, 0) to (0, -2) to (-2, 0), then [..F.. F.dr = (c) If C is the closed path in figure III along the boundary of a semi-disk of radius 2 oriented counterclockwise, then L.F. dr = √√2/2 -1 1 1 " -3 -4 1 -3 -1 || 2 4 -3 -4 -2 -1 ||| 1 3

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 21E
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Suppose F(x, y) = (4x + 2y)i + (2x + 4y)j. Evaluate the line integral for each of the given paths, which are comprised of line segments and arcs of circles. (a) If C is the open semicircular path in figure I of radius 2 oriented counterclockwise, then Jo F. . dr = (b) If C is the open piecewise linear path in figure II from (2,0) to (0, -2) to (-2, 0), then Jó F. dr = (c) If C is the closed path in figure III along the boundary of a semi-disk of radius 2 oriented counterclockwise, -4 then [F -4 ·dr = -3 -2 1 (Click on a graph to enlarge it.) -4 -3 II 1 2 3 -4 -3 ||| 4
Transcribed Image Text:Suppose F(x, y) = (4x + 2y)i + (2x + 4y)j. Evaluate the line integral for each of the given paths, which are comprised of line segments and arcs of circles. (a) If C is the open semicircular path in figure I of radius 2 oriented counterclockwise, then Jo F. . dr = (b) If C is the open piecewise linear path in figure II from (2,0) to (0, -2) to (-2, 0), then Jó F. dr = (c) If C is the closed path in figure III along the boundary of a semi-disk of radius 2 oriented counterclockwise, -4 then [F -4 ·dr = -3 -2 1 (Click on a graph to enlarge it.) -4 -3 II 1 2 3 -4 -3 ||| 4
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