Example 3 Let C be the closed curve consisting of the upper half-circle of radius 1 and the line forming its diameter along the x-axis, oriented counterclockwise. (See Figure 18.25.) Find fF dr where F (x, y) = -yi + aj. %3D 1 C1 C2 -1 1 Figure 18.25: The curve C C1 + C2 for Example 3

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 61E
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Example 3
Let C be the closed curve consisting of the upper half-circle of radius 1 and the line forming its
diameter along the x-axis, oriented counterclockwise. (See Figure 18.25.) Find lF dr where
F (r, y) = -yi + xj.
C1
C2
-1
1
Figure 18.25: The curve C = Cı + C2 for Example 3
Transcribed Image Text:Example 3 Let C be the closed curve consisting of the upper half-circle of radius 1 and the line forming its diameter along the x-axis, oriented counterclockwise. (See Figure 18.25.) Find lF dr where F (r, y) = -yi + xj. C1 C2 -1 1 Figure 18.25: The curve C = Cı + C2 for Example 3
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