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5. We consider a loop defined by y = x² from x= = 0 to x = 1, y = (1+x)/2 from x = 1 to x = 0, and x = 0 from y = 1/2 to y = 0. (See Figure 1). Determine the contour integral of F = (x + 2y, xy) along that loop using two different techniques: . a. direct calculation & F · dl and b. Stokes' method SS (V × F) · ñ d² A -0.5 -1:5 y = (1+x)/2 -0.5 x=0 0 y -0.5 0.5 y=x² X

5. We consider a loop defined by y = x² from x= = 0 to x = 1, y = (1+x)/2 from x = 1 to x = 0, and x = 0 from y = 1/2 to y = 0. (See Figure 1). Determine the contour integral of F = (x + 2y, xy) along that loop using two different techniques: . a. direct calculation & F · dl and b. Stokes' method SS (V × F) · ñ d² A -0.5 -1:5 y = (1+x)/2 -0.5 x=0 0 y -0.5 0.5 y=x² X

Algebra & Trigonometry with Analytic Geometry
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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5. We consider a loop defined by y = x² from x = 0 to x = 1, y = (1 + x)/2 from x = 1 to x = 0, and x = 0 from y = 1/2 to y = 0. (See Figure 1). Determine the contour integral of F (x + 2y, xy) along that loop using two different techniques: = a. direct calculation F. di and b. Stokes' method ff(xF). ñ d² A -0.5 -1-5- -1- y = (1+x)/2 -0.5 x=0 0 y -0.5 0.5 y=x² X
Transcribed Image Text:5. We consider a loop defined by y = x² from x = 0 to x = 1, y = (1 + x)/2 from x = 1 to x = 0, and x = 0 from y = 1/2 to y = 0. (See Figure 1). Determine the contour integral of F (x + 2y, xy) along that loop using two different techniques: = a. direct calculation F. di and b. Stokes' method ff(xF). ñ d² A -0.5 -1-5- -1- y = (1+x)/2 -0.5 x=0 0 y -0.5 0.5 y=x² X
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