Let C be the oriented closed curve composed of the two line segments: the line segment from (0,1) to (0,0), the line segment from (0,0) to (-1,0); and the arc of the parabola from (-1,0) to (0,1). Consider the vector-field y=1-x² F = x²yi - xy² j. Which of the following corresponds to f.F. F.dr using Green's Theorem? Caution: pay attention to the orientation!

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
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Let C be the oriented closed curve composed of the two line segments: the line
segment from (0,1) to (0,0), the line segment from (0,0) to (-1,0); and the arc of the
parabola
from (-1,0) to (0,1).
Consider the vector-field
y=1-x²
F=r²yi ry²j.
Which of the following corresponds to
fo
-
F.dr
using Green's Theorem?
Caution: pay attention to the orientation!
Transcribed Image Text:Let C be the oriented closed curve composed of the two line segments: the line segment from (0,1) to (0,0), the line segment from (0,0) to (-1,0); and the arc of the parabola from (-1,0) to (0,1). Consider the vector-field y=1-x² F=r²yi ry²j. Which of the following corresponds to fo - F.dr using Green's Theorem? Caution: pay attention to the orientation!
O b)
O
fF.d
f F
F.dr=
F.dr =
- S₁, S² * (2 ² + 1²³) dy dz
E
= 6₁² 6² ² ( 2² + y²³) dy dz
(8 2)
JT
10 10
f. F. dr =
f F-dr = 0
(x² + y²) dy dx
¯ ¯ ] } ]
(x² + y²) dy dr
f. F
F. dr = -₁ (a² + y²) dy da
Transcribed Image Text:O b) O fF.d f F F.dr= F.dr = - S₁, S² * (2 ² + 1²³) dy dz E = 6₁² 6² ² ( 2² + y²³) dy dz (8 2) JT 10 10 f. F. dr = f F-dr = 0 (x² + y²) dy dx ¯ ¯ ] } ] (x² + y²) dy dr f. F F. dr = -₁ (a² + y²) dy da
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