x² y² 9 4 2. Let C₁ be the ellipse + = 1 traced counterclockwise and C₂ be the paral- lelogram with vertices at (2, 1), (1,-1), (-1,-1), and (0, 1) traced clockwise. Define C = C₁ UC₂ F(x, y) = (1 − y, x + c³²). (a) (b) (c) [..F. Evaluate F. dR by direct computation. Use Green's Theorem to find the value of i [F-dk. [F.dR. Use (a) and (b) to find the value of

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 29E
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22
2. Let C₁ be the ellipse +
y²
9 4
lelogram with vertices at (2, 1), (1,−1), (−1, -1), and (0, 1) traced clockwise.
Define C=C₁UC₂
(a)
(b)
(c)
Evaluate
=
1 traced counterclockwise and C₂ be the paral-
F(x, y) =
Ja
x+ev²³).
= - y. x +
FdR by direct computation.
Use Green's Theorem to find the value of
Use (a) and (b) to find the value of
~?
L.F
F.dR.
F.dR.
2
Transcribed Image Text:22 2. Let C₁ be the ellipse + y² 9 4 lelogram with vertices at (2, 1), (1,−1), (−1, -1), and (0, 1) traced clockwise. Define C=C₁UC₂ (a) (b) (c) Evaluate = 1 traced counterclockwise and C₂ be the paral- F(x, y) = Ja x+ev²³). = - y. x + FdR by direct computation. Use Green's Theorem to find the value of Use (a) and (b) to find the value of ~? L.F F.dR. F.dR. 2
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